Research

Monograph

1. Matteo Dalla Riva, Massimo Lanza de Cristoforis, and Paolo Musolino. Singularly Perturbed Boundary Value Problems: A Functional Analytic Approach. Springer, Cham, 2021. eBook ISBN: 978-3-030-76259-9, DOI: 10.1007/978-3-030-76259-9, Hard- cover ISBN: 978-3-030-76258-2, iv+676. Book

Papers in scientific journals

1. Matteo Dalla Riva, Paolo Luzzini, Riccardo Molinarolo and Paolo Musolino, Multi-parameter perturbations for the space-periodic heat equation, Comm. Pure Appl. Anal., 23 (2), 144-164, 2024. DOI: 10.3934/cpaa.2024004 Paper Preprint

2. Laura Abatangelo, Corentin Léna, and Paolo Musolino, Asymptotic behavior of generalized capacities with applications to eigenvalue perturbations: the higher dimensional case. Nonlinear Anal., Vol. 238, Paper No. 113391, 2024. DOI: 10.1016/j.na.2023.113391. Paper Preprint

3. Roberto Bramati, Matteo Dalla Riva, Paolo Luzzini, and Paolo Musolino, The Functional Analytic Approach for Quasi-periodic Boundary Value Problems for the Helmholtz equation.  Adv. Differential Equations, 29(1-2): 27–68, 2024. DOI: 10.57262/ade029-0102-27. Paper Preprint 

4. Paolo Musolino, Martin Dutko, and Gennady Mishuris, Asymptotic analysis of perturbed Robin problems in a planar domain. Electron. J. Differential Equations, Vol. 2023, No. 57, pp. 1-21, 2023. DOI: 10.58997/ejde.2023.57 Paper Preprint

5. Matteo Dalla Riva, Gennady Mishuris, and Paolo Musolino, A degenerating Robin-type traction problem in a periodic domain. Math. Model. Anal., 28(3), 509–521, 2023. DOI: 10.3846/mma.2023.17681 Paper Preprint 

6. Matteo Dalla Riva, Paolo Luzzini, and Paolo Musolino, Singular behavior for a multi-parameter periodic Dirichlet problem. Asymptot. Anal., 134, no. 1-2, pp. 193-212, 2023. DOI: 10.3233/ASY- 231831 Paper Preprint 

7. Matteo Dalla Riva, Gennady Mishuris, and Paolo Musolino, Integral equation method for a Robin-type traction problem in a periodic domain. Trans. A. Razmadze Math. Inst., 176 (3), 349-360, 2022. Paper Preprint

8. Matteo Dalla Riva, Riccardo Molinarolo, and Paolo Musolino. Existence results for a nonlinear nonautonomus transmission problem via domain perturbation.  Proc. Roy. Soc. Edinburgh Sect. A,  152 (6), 1451–1476, 2022. DOI: 10.1017/prm.2021.60 Paper Preprint

9. Laura Abatangelo, Corentin Léna, and Paolo Musolino, Ramification of multiple eigenvalues for the Dirichlet-Laplacian in perforated domains. J. Funct. Anal., 283 (12), Paper No.109718, 50 pp, 2022. DOI: 10.1016/j.jfa.2022.109718 Paper Preprint

10. Paolo Musolino and Gennady Mishuris, Interaction of scales for a singularly perturbed degenerating nonlinear Robin problem. Philos. Trans. Roy. Soc. A, 380 (2236), 18 pp., 2022. DOI: 10.1098/rsta.2022.0159 Paper Preprint

11. Matteo Dalla Riva, Paolo Luzzini, and Paolo Musolino, Shape analyticity and singular perturbations for layer potential operators, ESAIM Math. Model. Numer. Anal., 56 (6), 1889–1910, 2022. DOI: 10.1051/m2an/2022057. Paper Preprint

12. Matteo Dalla Riva, Paolo Luzzini, and Paolo Musolino, Multi-parameter analysis of the obstacle scattering problem, Inverse Problems, 38, 055004, 17 pp., 2022. DOI: 10.1088/1361-6420/ac5eea Paper Preprint 

13. Pier Domenico Lamberti, Paolo Luzzini, and Paolo Musolino. Shape perturbation of Grushin eigenvalues. J. Geom. Anal.,  31 (11), 10679--10717, 2021.  DOI: 10.1007/s12220-021-00662-9 Paper Preprint

14. Massimo Lanza de Cristoforis, Paolo Musolino, and Jari Taskinen. A real analyticity result for symmetric functions of the eigenvalues of a quasiperiodic spectral problem for the Dirichlet Laplacian. J. Operator Theory, 86 (2), 439--467, 2021. DOI: 10.7900/jot.2020jun08.2304 Paper Preprint

15. Laura Abatangelo, Virginie Bonnaillie-Noël, Corentin Léna, and Paolo Musolino. Asymptotic behavior of $u$-capacities and singular perturbations for the Dirichlet-Laplacian. ESAIM Control Optim. Calc. Var.,  27, suppl., Paper No. S25, 43 pp., 2021. DOI: 10.1051/cocv/2020078 Paper Preprint

16. Virginie Bonnaillie-Noël,  Matteo Dalla Riva, Marc Dambrine, and Paolo Musolino. Global representation and multi-scale expansion for the Dirichlet problem in a domain with a small hole close to the boundary. Comm. Partial Differential Equations, 46 (2), 282--309, 2021. DOI: 10.1080/03605302.2020.1840585  Paper Preprint

17. Riccardo Falconi, Paolo Luzzini, and Paolo Musolino. Asymptotic behavior of integral functionals for a two-parameter singularly perturbed nonlinear traction problem. Math. Methods Appl. Sci., 44 (2), 2111--2129, 2021. DOI: 10.1002/mma.6920 Paper Preprint

18. Paolo Luzzini and Paolo Musolino. Perturbation analysis of the effective conductivity of a periodic composite. Net. Heterog. Media, 15 (4), 581–603, 2020. DOI: 10.3934/nhm.2020015 Paper Preprint

19. Matteo Dalla Riva, Massimo Lanza de Cristoforis and Paolo Musolino. Mapping properties of weakly singular periodic volume potentials  in Roumieu classes. J. Integral Equations Appl.,   32 (2), 129–149, 2020. DOI: 10.1216/jie.2020.32.129 Paper Preprint

20. Matteo Dalla Riva, Riccardo Molinarolo and Paolo Musolino. Local uniqueness of the solutions for a singularly perturbed nonlinear nonautonomous transmission problem.  Nonlinear Anal. 191, 111645, 2020. DOI: 10.1016/j.na.2019.111645 Paper Preprint

21. Paolo Luzzini, Paolo Musolino, and Roman Pukhtaievych. Shape analysis of the longitudinal flow along a periodic array of cylinders. J. Math. Anal. Appl.,  477 (2), 1369–1395, 2019. DOI: 10.1016/j.jmaa.2019.05.017 Paper Preprint

22. Massimo Lanza de Cristoforis and Paolo Musolino. Asymptotic behavior of the energy integral of a two-parameter  homogenization problem with nonlinear periodic Robin boundary conditions.  Proc. Edinb. Math. Soc. (2),  62 (4), 985-1016, 2019. DOI: 10.1017/S0013091518000858 Paper Preprint

23. Matteo Dalla Riva, Paolo Musolino, and Roman Pukhtaievych. Series expansion for the effective conductivity of a  periodic dilute composite with thermal resistance at the two-phase interface. Asymptot. Anal., 111 (3--4), 217--250, 2019. DOI: 10.3233/ASY-181495. Paper Preprint

24. Paolo Musolino and Gennady Mishuris. A nonlinear problem for the Laplace equation with a degenerating Robin condition. Math. Methods Appl. Sci., 41 (13), 5211–5229, 2018. DOI: 10.1002/mma.5072. Paper Preprint

25. Massimo Lanza de Cristoforis and Paolo Musolino. Analytic dependence of a periodic analog of a fundamental solution upon the periodicity parameters. Ann. Mat. Pura Appl., 197 (4), 1089–1116, 2018. DOI: 10.1007/s10231-017-0715-7.  Paper Preprint

26. Massimo Lanza de Cristoforis and Paolo Musolino. Two-parameter anisotropic homogenization for a Dirichlet problem for the Poisson equation in an unbounded periodically perforated domain. A functional analytic approach. Math. Nachr., 291 (8—9): 1310–1341, 2018. DOI: 10.1002/mana.201600414. Paper Preprint

27. Virginie Bonnaillie-Noël,  Matteo Dalla Riva, Marc Dambrine, and Paolo Musolino. A Dirichlet problem for the Laplace operator in a domain with a small hole close to the boundary. J. Math. Pures Appl. (9), 116, 211–267, 2018. DOI: 10.1016/j.matpur.2018.01.004. Paper Preprint

28. Massimo Lanza de Cristoforis and Paolo Musolino. Two-parameter homogenization for a nonlinear Robin problem for the Poisson equation in an unbounded periodically perforated domain. A functional analytic approach. Rev. Mat. Complut., 31(1): 63–110, 2018. DOI: 10.1007/s13163-017-0242-5 Paper Preprint

29. Matteo Dalla Riva and Paolo Musolino. Moderately close Neumann inclusions for the Poisson equation.  Math. Methods Appl. Sci., 41(3): 986–993, 2018.  DOI: 10.1002/mma.4028 Paper Preprint

30. Martin Costabel, Matteo Dalla Riva, Monique Dauge, and Paolo Musolino. Converging expansions for Lipschitz self-similar perforations of a plane sector. Integral Equations Operator Theory,  88 (3): 401–449, 2017. DOI: 10.1007/s00020-017-2377-7 Paper Preprint

31. Matteo Dalla Riva and Paolo Musolino. The Dirichlet problem in a planar domain with two moderately close holes. J. Differential Equations, 263 (5):2567–2605, 2017. DOI: 10.1016/j.jde.2017.04.006 Paper Preprint

32. Matteo Dalla Riva and Paolo Musolino. A mixed problem for the Laplace operator in a domain with moderately close holes. Comm. Partial Differential Equations, 41(5):812--837, 2016. DOI: 10.1080/03605302.2015.1135166 Paper Preprint

33. Massimo Lanza de Cristoforis and Paolo Musolino. A singularly perturbed Neumann problem for the Poisson equation in a periodically perforated domain. A functional analytic approach. ZAMM Z. Angew. Math. Mech.,  96(2), 253--272, 2016. DOI: 10.1002/zamm.201400035 Paper Preprint

34. Paolo Musolino and Vladimir Mityushev. Asymptotic behavior of the longitudinal permeability of a periodic array of thin cylinders. Electron. J. Differential Equations, 2015(290): 1-20, 2015. Paper Preprint

35. Matteo Dalla Riva, Massimo Lanza de Cristoforis and Paolo Musolino. Analytic dependence of volume potentials corresponding to parametric families of fundamental solution. Integral Equations Operator Theory, 82(3):371--393, 2015. DOI:10.1007/s00020-015-2236-3 Paper Preprint

36. Matteo Dalla Riva, Paolo Musolino and Sergei V. Rogosin. Series expansions for the solution of the Dirichlet problem in a planar domain with a small hole. Asymptot. Anal., 92(3-4):339-361, 2015. DOI: 10.3233/ASY-151283 Paper Preprint

37. Matteo Dalla Riva and Paolo Musolino. Real analytic families of harmonic functions in a planar domain with a small hole.  J. Math. Anal. Appl., 422(1):37-55, 2015. DOI: 10.1016/j.jmaa.2014.08.037 Paper Preprint

38. Matteo Dalla Riva and Paolo Musolino. Local uniqueness for singularly perturbed periodic nonlinear traction problems. Electron. J. Differential Equations, 2014(242): 1-14, 2014. Paper Preprint

39. Massimo Lanza de Cristoforis and Paolo Musolino. A quasi-linear heat transmission problem in a periodic two-phase dilute composite. A functional analytic approach. Comm. Pure Appl. Anal., 13(6):2509-2542, 2014. DOI: 10.3934/cpaa.2014.13.2509 Paper Preprint

40. Matteo Dalla Riva and Paolo Musolino. A singularly perturbed nonlinear traction problem in a periodically perforated domain: a functional analytic approach. Math. Methods Appl. Sci., 37(1):106-122, 2014. DOI: 10.1002/mma.2788 Paper Preprint

41. Matteo Dalla Riva, João Morais, and Paolo Musolino. A family of fundamental solutions of elliptic partial differential operators with quaternion constant coefficients. Math. Methods Appl. Sci., 36(12):1569-1582, 2013. DOI: 10.1002/mma.2706 Paper Preprint

42. Massimo Lanza de Cristoforis and Paolo Musolino. A real analyticity result for a nonlinear integral operator. J. Integral Equations Appl., 25(1):21-46, 2013. DOI: 10.1216/JIE-2013-25-1-21 Paper Preprint

43. Massimo Lanza de Cristoforis and Paolo Musolino. A singularly perturbed nonlinear Robin problem in a periodically perforated domain: a functional analytic approach. Complex Var. Elliptic Equ., 58(4):511-536, 2013. DOI: 10.1080/17476933.2011.638716 Paper Preprint

44. Matteo Dalla Riva and Paolo Musolino. A singularly perturbed non-ideal transmission problem and application to the effective conductivity of a periodic composite. SIAM J. Appl. Math., 73(1):24-46, 2013. DOI: 10.1137/120886637 Paper Preprint

45. Matteo Dalla Riva and Paolo Musolino. Real analytic families of harmonic functions in a domain with a small hole. J. Differential Equations, 252(12):6337-6355, 2012. DOI: 10.1016/j.jde.2012.03.0073 Paper Preprint

46. Paolo Musolino. A singularly perturbed Dirichlet problem for the Laplace operator in a periodically perforated domain. A functional analytic approach. Math. Methods Appl. Sci., 35(3): 334-349, 2012. DOI: 10.1002/mma.1575 Paper Preprint

47. Massimo Lanza de Cristoforis and Paolo Musolino. A perturbation result for periodic layer potentials of general second order differential operators with constant coefficients. Far East J. Math. Sci. (FJMS), 52(1):75-120, 2011 Paper Preprint

Papers in books and proceedings

1. Matteo Dalla Riva, Paolo Luzzini, and Paolo Musolino, A perturbation result for a Neumann problem in a periodic domain, In Analysis, Applications, and Computations - Selected contributions of the 13th ISAAC Congress, Ghent, Belgium, 2021. Research Perspectives, pages 271-282, Birkhäuser, Cham, 2023. DOI: 10.1007/978-3-031-36375-7_20. Paper Preprint

2. Paolo Luzzini and Paolo Musolino. Domain perturbation for the solution of a periodic Dirichlet problem. In P. Cerejeiras, M. Reissig. I. Sabadini, J. Toft, Editors, Current Trends in Analysis, its Applications and Computation, Proceedings of the 12th ISAAC congress (Aveiro, 2019). Trends in Mathematics. Research Perspectives, pages 181-189, Birkhäuser, Cham, 2022. DOI: 10.1007/978-3-030-87502-2_18 Paper Preprint

3. Paolo Luzzini, Paolo Musolino, and Roman Pukhtaievych. Real analyticity of periodic layer potentials upon perturbation of the periodicity parameters and of the support. In P. Cerejeiras, M. Reissig. I. Sabadini, J. Toft, Editors, Current Trends in Analysis, its Applications and Computation, Proceedings of the 12th ISAAC congress (Aveiro, 2019). Trends in Mathematics. Research Perspectives, pages 191-199, Birkhäuser, Cham, 2022. DOI: 10.1007/978-3-030-87502-2_19 Paper Preprint

4. Matteo Dalla Riva, Paolo Luzzini, Paolo Musolino, and Roman Pukhtaievych. Dependence of effective properties upon regular perturbations. In I. Andrianov, S. Gluzman, V. Mityushev, Editors, Mechanics and Physics of Structured Media, pages 271-301, Elsevier, 2022. DOI: 10.1016/B978-0-32-390543-5.00019-0 Paper Preprint

5. S. E. Mikhailov, P. Musolino and J. Orlik. Rescaling and trace operators in fractional Sobolev spaces on bounded Lipschitz domains with periodic structure. In C. Constanda and P.J. Harris, editors, Integral Methods in Science and Engineering, Proceedings of the 15th International Conference on Integral Methods in Science and Engineering, IMSE 2018, Brighton, UK, 16-20 July 2018, pages 237-251,  Birkhäuser Verlag, Basel, 2019. DOI: 10.1007/978-3-030-16077-7_19 Paper Preprint

6. Paolo Luzzini and Paolo Musolino. Periodic transmission problems for the heat equation. In C. Constanda and P.J. Harris, editors, Integral Methods in Science and Engineering, Proceedings of the 15th International Conference on Integral Methods in Science and Engineering, IMSE 2018, Brighton, UK, 16-20 July 2018, pages 211-223, Birkhäuser Verlag, Basel, 2019. DOI: 10.1007/978-3-030-16077-7_17 Paper Preprint

7. Matteo Dalla Riva, Massimo Lanza de Cristoforis and Paolo Musolino. A local uniqueness result for a  quasi-linear heat transmission problem in a periodic two-phase dilute composite. In Vladimir Maz'ya, David Natroshvili, Eugene Shargorodsky, Wolfgang L. Wendland, editors, Recent Trends in Operator Theory and Partial Differential Equations - The Roland Duduchava Anniversary Volume, Operator Theory: Advances and Applications, Volume 258, pages 193–227, Birkhäuser Verlag, Basel, 2017. DOI: 10.1007/978-3-319-47079- 5_10 Paper Preprint

8. Massimo Lanza de Cristoforis and Paolo Musolino. A functional analytic approach to homogenization problems. In C. Constanda and A. Kirsch, editors, Integral Methods in Science and Engineering: Theoretical and Computational Advances, Proceedings of the 13th International Conference on Integral Methods in Science and Engineering, IMSE 2014, Karlsruhe, Germany 21-25 July 2014, pages 353-359, Birkhäuser Verlag, Basel, 2015. DOI: 10.1007/978-3-319-16727-5_30 Paper Preprint

9. Matteo Dalla Riva and Paolo Musolino. Harmonic functions in a domain with a small hole. A functional analytic approach. In C. Constanda and A. Kirsch, editors, Integral Methods in Science and Engineering: Theoretical and Computational Advances, Proceedings of the 13th International Conference on Integral Methods in Science and Engineering, IMSE 2014, Karlsruhe, Germany 21-25 July 2014, pages 143-153, Birkhäuser Verlag, Basel, 2015. DOI: 10.1007/978-3-319-16727-5_13  Paper Preprint

10. Matteo Dalla Riva and Paolo Musolino. Energy integral of a nonlinear traction problem in a singularly perturbed periodically perforated domain. In T.Aliyev, A.Golberg, and S.V.Rogosin, editors, Complex Analysis and Potential Theory with applications, Proceedings of the 9th ISAAC Congress,  Krakow, Poland 5-9 August, 2013, pages 41–52, Cambridge Scientific Publishers, Cottenham, UK, 2014. Order to publisher Preprint

11. Matteo Dalla Riva and Paolo Musolino. Energy integral of the solution of a non-ideal transmission problem in a singularly perturbed periodic domain. In T.Aliyev, A.Golberg, and S.V.Rogosin, editors, Complex Analysis and Potential Theory with applications, Proceedings of the 9th ISAAC Congress,  Krakow, Poland 5-9 August, 2013, pages 31–40, Cambridge Scientific Publishers, Cottenham, UK, 2014. Order to publisher Preprint

12. Matteo Dalla Riva, Massimo Lanza de Cristoforis, and Paolo Musolino. On a singularly perturbed periodic nonlinear Robin problem. In M.V.Dubatovskaya, S.V.Rogosin, editors, Analytical Methods of Analysis and Differential Equations: AMADE 2012, pages 73–92, Cambridge Scientific Publishers, Cottenham, UK, 2014. Order to publisher Preprint

13. Paolo Musolino. A singularly perturbed Dirichlet problem for the Poisson equation in a periodically perforated domain. A functional analytic approach. In Alexandre Almeida, Luis Castro, Frank-Olme Speck, editors, Advances in Harmonic Analysis and Operator Theory, The Stefan Samko Anniversary Volume, Operator Theory: Advances and Applications, Volume 229, pages 269-289, Birkhäuser Verlag, Basel, 2013. DOI: 10.1007/978-3-0348-0516-2_15 Paper Preprint

14. Matteo Dalla Riva and Paolo Musolino. Effective conductivity of a singularly perturbed periodic two-phase composite with imperfect thermal contact at the two-phase interface. In S. Sivasundaram, editor, 9th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences: ICNPAA 2012, Vienna, Austria, 10-14 July 2012. AIP Conference Proceedings vol. 1493, pages 264-268. American Institute of Physics, Melville, NY, 2012. DOI: 10.1063/1.4765499 Paper Preprint

15. Matteo Dalla Riva, João Morais, and Paolo Musolino. A family of fundamental solutions for elliptic quaternion coefficient differential operators and application to perturbation results for single layer potentials. In S. Sivasundaram, editor, 9th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences: ICNPAA 2012, Vienna, Austria, 10-14 July 2012. AIP Conference Proceedings vol. 1493, pages 269-273. American Institute of Physics, Melville, NY, 2012. DOI: 10.1063/1.4765500 Paper Preprint

16. Paolo Musolino. A functional analytic approach for a singularly perturbed Dirichlet problem for the Laplace operator in a periodically perforated domain. In T. E. Simos, G. Psihoyios, and Ch. Tsitouras, editors, Numerical analysis and applied mathematics. International conference of numerical analysis and applied mathematics (ICNAAM 2010), Rhodes, Greece, 19-25 September 2010. AIP Conference Proceedings vol. 1281, pages 928-931. American Institute of Physics, Melville, NY, 2010. DOI: 10.1063/1.3498645 Paper Preprint 

Other publications

1. Matteo Dalla Riva, Pier Domenico Lamberti, Paolo Musolino, and Sergei V. Rogosin,  A tribute to Massimo Lanza de Cristoforis. Complex Var. Elliptic Equ., 65 (1): no. 1, 1-5, 2020. DOI: 10.1080/17476933.2019.1655553 Paper Preprint

2. Paolo Musolino, Problemi di perturbazione singolare e di omogeneizzazione in un dominio periodicamente perforato. Un approccio funzionale analitico, La Matematica nella Società e nella Cultura, 6(3):517-520, 2013. Paper Preprint

Edited books

1. Christian Constanda, Matteo Dalla Riva, Pier Domenico Lamberti, Paolo Musolino (editors). Integral Methods in Science and Engineering, Volume 2 - Practical Applications. Birkhäuser Basel, 2017. ISBN: 978-3-319-59386-9, DOI: 10.1007/978-3-319-59387-6 Book

2. Christian Constanda, Matteo Dalla Riva, Pier Domenico Lamberti, Paolo Musolino (editors). Integral Methods in Science and Engineering, Volume 1 - Theoretical Techniques. Birkhäuser Basel, 2017. ISBN: 978-3-319-59383-8, DOI: 10.1007/978-3-319-59384-5 Book

Submitted papers

     Collaborators

1. Laura Abatangelo

2. Virginie Bonnaillie-Noël

3. Roberto Bramati

4. Martin Costabel

5. Matteo Dalla Riva

6. Marc Dambrine

7. Monique Dauge

8. Martin Dutko

9. Riccardo Falconi

10. Pier Domenico Lamberti

11. Massimo Lanza de Cristoforis

12. Corentin Léna

13. Paolo Luzzini

14. Sergey Mikhailov

15. Gennady Mishuris

16. Vladimir Mityushev

17. Riccardo Molinarolo

18. João Pedro Morais

19. Julia Orlik

20. Roman Pukhtaievych

21. Sergei V. Rogosin

22. Jari Taskinen