Nonlinear Potential Theory on Manifolds;

Regularity of Elliptic PDE's and Systems, functionals;

Parabolic Equations and Systems;

Viscosity Theory for Fully Nonlinear Equations;

Equations in  Carnot Groups with applications to Finance;

Variational models for liquid crystals.

Asymptotic mean value formulas for the p-Laplacian.

Submitted/In progress

[Lee, M., Ok, J., S.B.] “ Lipschitz regularity for orthotropic functionals with general growth “, arXiv:2607.04773.

[Canevari, G., Dipasquale, F., S.B.] “The formation of gradient-driven singular structures of codimension one and two in two-dimensions: The case study of ferronematics. Part~{II}: Refined structure of the energy-concentration set”, arXiv:2606.12644.

[Canevari, G., Dipasquale, F., S.B.] “Liftings of Sobolev maps into closed Riemannian manifolds via double coverings and minimal connections relative to planar sets, with an application to ferronematics”, arXiv:2603.01985.

[Canevari, G., Dipasquale, F., S.B.] “ The formation of gradient-driven singular structures of codimension one and two in two-dimensions: The case study of ferronematics. Part~I: Energy estimates and compactness results”, arXiv:2505.07506.

[Scilla, G., S.B.] “Orlicz meets double phase: steady fluids”.

[ Acharya, A., S.B., Zarnescu, A.] “Variational dual solutions for incompressible fluids ", arXiv:2409.04911.

[Citti, G., S.B.] “ Internal Schauder estimates for Hörmander type equations with Dini continuous source ", submitted.

[Ok, J., Scilla, G., S.B.] “Partial regularity for  parabolic systems of double phase type", arXiv:2510.03849.

[Ball, J.B., Canevari, G., S.B.] "A variational model for smectics ". in progress. 

[Bresciani, M., S.B.] 2025. "Quasistatic evolution of Orlicz–Sobolev nematic elastomers", May 2025, Annali di Matematica Pura e Applicata. 

[Ok, J., Scilla, G., S.B.] 2025. "Partial regularity for general systems of double phase type with continuous coefficients ". July 2025, Journal of Differential Equations, Volume 432.

[S.B.] 2025.  Chapter : "Asymptotic mean value formulas for the p-Laplacian in the Euclidean space and in the Heisenberg Group" in the volume " Direct and Inverse problems with applications",Trends in Mathematics, Birkhauser Cham,Hardcover ISBN978-3-031-98644-4.(PhD course in Ghent).

Variational and PDE Methods in Nonlinear Science,book published by Springer. Lecture Notes in Mathematics (CIME Foundation Subseries, Volume 2366). The book’s editors and directors are F. Béthuel, G. Orlandi, and B. Stroffolini. 

[Dipasquale, F.,S.B. ] 2024.“ Manifold -constrained free discontinuity problems and Sobolev approximation", Nonlinear Anal. TMA 247 113597.

[Ok, J., Scilla, G., S.B. ] 2024. “ Partial regularity results for degenerate parabolic systems with general growth via caloric approximations ", Calc. Var and PDEs, 63:105 .

[Biagi, S.. Bramanti,M., S.B.] 2024. “ KFP operators with coefficients measurable in time and Dini continuous in space ",  J. Evol. Equ. 24:32.

[Ok, J.,  Scilla, G., S.B. ] 2024. “Regularity theory for parabolic systems with Uhlenbeck structure", Journal de Mathématiques Pures et Appl.  182, pp. 116–163.

[Canevari, G., Majumdar, A.,S.B.,Wang, Y.] 2023. “Two-dimensional Ferronematics, Canonical Harmonic Maps and Minimal Connections “,  Archive for Rational Mechanics and Analysis, 247(6), 110.

[Scilla,G.,Solombrino, F.,S.B.] 2023.”Integral representation and Gamma-convergence for  energies in linear elasticity with p(x)-growth and surface discontinuities", Calc. Var. and PDEs,(62(8), 213.

[Scilla, G., S.B.] 2023. “ Partial regularity for steady double phase fluids”, Mathematics in Engineering, Volume 5, Issue 5: 1-47. 

[Ball, J., Canevari, G., S.B.] 2023. ”A free discontinuity model for smectic thin films “, Liquid Crystals, Volume 50,  Issue 7-10 , 1439–1448, Taylor & Francis.

[De Filippis, C., S.B.] 2023. “Singular Multiple Integrals and Nonlinear Potentials”,  Journal of Functional Analysis, 285, 109952.

[Domokos, A., Manfredi, J., Ricciotti, D., S.B.] 2023. “ Boundary convergence properties for $L^p$- averages" , J. Math. Sci., New York ,vol. 269, No. 6, pp. 778-791.

Ok, J. Scilla, G., S.B. ]  2022. “ Boundary Partial Holder Regularity for Minimizers of Discontinuous Quasiconvex Integrals with VMO Coefficients and General Growth”, Communications on Pure and Applied Analysis,  Volume 21, Issue 12: 4173-4214.

[Domokos, A., Manfredi, J., Ricciotti, D., S.B.]  2022. “Convergence of the natural p-means for the p-Laplacian in the Heisenberg Group", Nonlinear Analysis, Volume 223.

[Scilla, G., S.B. ]  2022. “ Invertibility of Orlicz-Sobolev maps”, In: Español, M.I., Lewicka, M., Scardia, L., Schlömerkemper, A. (eds) Research in Mathematics of Materials Science. Association for Women in Mathematics Series, vol 31. Springer, Cham. p 297–317.

[Polidoro, S., Rebucci, A., S.B.]  2022. “ Schauder type estimates for degenerate Kolmogorov equations with Dini continuous coefficients", Communications on Pure and Applied Analysis, 21(4),  1385–1416 . 

[Goodrich, C., Scilla, G., S.B.] 2021.”Partial regularity for minimizers of discontinuous quasiconvex integrals with general growth”, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, pp. 1 - 42.

[Manfredi, J., S.B.] 2021. “Convergence of the natural p-means for the p-Laplacian", ESAIM COCV, 27  2021026.

[S.B.] 2020. “ Partial Regularity results for quasimonotone elliptic systems with general growth", Zeitschrift fur Analysis und ihre Anwendungen,39, issue 3,Pages 315 - 347.

[Scilla, G., S.B.] 2020. “Relaxation of nonlinear elastic energies related to Orlicz-Sobolev nematic elastomers", Rend. Lincei Mat. Appl. 31, 349--388.

[Henao, D., S.B.] 2020. “ Orlicz-Sobolev nematic elastomers", Nonlinear Analysis,194,111513.

[Canevari, G., Majumdar, A., S.B.] 2019. “ Minimizers of a Landau-de Gennes Energy with a Subquadratic Elastic Energy ",Arch. Rational Mech. Anal. 233, 1169–1210.

[Diening, L., Schwarzacher, S., S.B.,Verde,A.]  2017. “ Parabolic Lipschitz truncation and Caloric Approximation", Calc. Var. Partial Differential Equations,  56 , no. 4, 56:120.

[Beck, L., S.B.] 2013. “ Regularity results for differential forms solving degenerate elliptic systems “, Calculus  of  Var.  and Partial Differential Equations,  46 ,  no. 3-4, 769-–808.

[Diening, L., Lengeler, D.,S.B.,Verde,A.] 2012. “ Partial regularity for minimizers of quasiconvex functionals with general growth",  SIAM Journal on Mathematical Analysis, 44  no. 5, 3594-–3616.

[Diening, L., S.B.,Verde,A.]  2012. “The phi-harmonic approximation and the regularity of phi-harmonic maps” , Journal of Differential Equations, 253,  1943--1958.

[Diening, L., S.B.,Verde,A.] 2009. “ Everywhere Regularity of functionals with phi-growth",  Manuscripta Math.  129, no. 4, 449--481.

[Juutinen, P., Lu, G.,  Manfredi, J., S.B.] 2007. “ Convex functions on Carnot groups",  Rev. Mat. Iberoam. 23 , no. 1, 191--200. 

[Lu, G., Manfredi, J., S.B.] 2004. “ Convex functions on the Heisenberg group",  Calc. Var. Partial Differential Equations 19,  no. 1, 1--22. 

[Manfredi, J., S.B.] 2002. “A version of the Hopf-Lax formula in the Heisenberg group",  Comm. Partial Differential Equations 27 , no. 5-6, 1139--1159. 

 [Iwaniec, T., Scott, C., S.B.] 1999. “ Nonlinear Hodge theory on manifolds with boundary",  Ann. Mat. Pura Appl. (4) 177 , 37--115.  

[Cianchi, A., S.B.] 1998. “ An extension of Hedberg's convolution inequality and applications",  J. Math. Anal. Appl. 227, no. 1, 166--186. 

[Greco, L., Iwaniec, T., Sbordone, C.,S.B.] 1995. “ Degree formulas for maps with nonintegrable Jacobian",  Topol. Methods Nonlinear Anal. 6 , no. 1, 81--95.  

[S.B.] 1991. “Global boundedness of solutions of anisotropic variational problems",  Boll. Un. Mat. Ital. A (7) 5  no. 3, 345--352.