Research interests, Publications, and CV

Curriculum Vitae

Full CV here 

Research interests

- Complex dynamics in problems of celestial mechanics; see publications [1, 2, 4, 8].

- Qualitative properties of solutions to elliptic equations and systems; see publications [3, 5, 7, 10, 14, 23, 27, 29, 33, 35] and preprints [3, 5].

- Existence of solutions via variational and perturbative methods; see publications [6, 9, 13, 15, 17, 19, 24, 28, 30, 31, 32, 34, 37, 39] and preprint [2].

- Regularity for solutions to singularly perturbed systems, and associated free-boundary problems; publications [11, 12, 16, 21, 22, 26, 36, 38] and preprint [1].

- Regularity and qualitative properties of solutions to non-local equations; publications [18, 20, 25] and preprint [4]


Preprints and publications:

All my preprints and papers are available on arXiv.


Preprints:

5) F. Esposito, B. Sciunzi and N. Soave. Notes on overdetermined singular problems. Accepted for publication on Bulletin of the London Mathematical Society. Link 

4) S. Dipierro, N. Soave and E. Valdinoci. A fractional Hopf Lemma for sign-changing solutions. Link 

3) M. Muratori and N. Soave. Radial solutions of the Lane-Emden system on Cartan-Hadamard manifolds: asymptotics and rigidity. Link 

2) J. Borthwick, X. Chang, L. Jeanjean and N. Soave. Bounded Palais-Smale sequences with Morse-type information for some constrained functionals. Link 

1) N. Soave and G. Tortone. On the nodal set of solutions to some sublinear equations without homogeneity. Link 


Publications on international journals:

39) X. Chang, L. Jeanjean and N. Soave. Normalized solutions of L^2-supercritical NLS equations on compact metric graphs. Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire. Doi: 10.4171/AIHPC/88. Link

38) N. Soave and S. Terracini. An anisotropic monotoncity formula, with applications to some segregation problems. Journal of the European Mathematical Society, 25(9): 3727--3765, 2023. Doi: 10.4171/JEMS/1270. Link

37) J. Borthwick, X. Chang, L. Jeanjean and N. Soave. Normalized solutions of L^2-supercritical NLS equations on noncompact metric graphs with localized nonlinearities. Nonlinearity, 36: 3776-3795, 2023. Doi: 10.1088/1361-6544/acda76. Link 

36) N. Soave, H. Tavares and A. Zilio. Free boundary problems with long-range interactions: uniform Lipschitz estimates in the radius. Mathematische Annalen 386: 551--585, 2023. Doi: 10.1007/s00208-022-02406-8 Link

35) M. Muratori and N. Soave. Some rigidity results for Sobolev inequalities and related PDEs on Cartan-Hadamard manifolds. Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. XXIV(2): 751--792, 2023. Doi: 10.2422/2036-2145.202105\_071 Link

34) D. Pierotti and N. Soave. Ground states for the NLS equation with combined nonlinearities on non-compact metric graphs. SIAM Journal of Mathematical Analysis 54(1): 768-790, 2022. Doi: 10.1137/20M1377837 Link

33) E. Moreira Dos Santos, G. Nornberg, N. Soave. On unique continuation principles for some elliptic systems. Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire, 38(5): 1667-1680, 2021. Doi: 10.1016/j-anihpc.2020.12.001 Link

32) D. Pierotti, N. Soave and G. Verzini. Local minimizers in absence of ground states for the critical NLS energy on metric graphs. Accepted for publication on Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 151(2): 705-733, 2021.  Doi: 10.1017/prm.2020.36. Link

31) N. Soave. Normalized ground states for the NLS equation with combined nonlinearities. Journal of Differential Equations, 269 (9), 6941--6987, 2020. Doi: 10.1016/j.jde.2020.05.016 Link

30) N. Soave. Normalized ground states for the NLS equation with combined nonlinearities: the Sobolev critical case. Journal of Functional Analysis, 279 (6), 108610, 2020. Doi: 10.1016/j.jfa.2020.108610 Link

29) N. Soave. Saddle-shaped positive solutions for elliptic systems with bistable nonlinearity. Mathematics in Engineering, 2 (3), 423--437, 2020. Doi: 10.3934/mine.2020019. Link

28) A. Pistoia, N. Soave and H. Tavares. A fountain of positive Bubbles on a Coron's Problem for a Competitive Weakly Coupled Gradient System. Journal de Mathématiques Pures et Appliquées, 135: 159-198, 2020. Doi: 10.1016/j.matpur.2019.09.004. Link

27) A. Farina, B. Sciunzi and N. Soave, Monotonicity and rigidity of solutions to some elliptic systems with uniform limits. Communications in Contemporary Mathematics, 22 (5): 1950044, 24 pages, 2020. Doi: 10.1142/S0219199719500445. Link

26) N. Soave and S. Terracini. The nodal set of solutions to some elliptic problems: singular nonlinearities. Journal de Mathématiques Pures et Appliquées, 128: 264--296, 2019. Doi: 10.1016/j.matpur.2019.06.009. Link

25) N. Soave and E. Valdinoci, Overdetermined problems for the fractional Laplacian in exterior and annular sets. Journal d'Analyse Mathématique, 137 (1): 101--134, 2019. Doi: 10.1007/s11854-018-0067-2. Link

24) T. Bartsch and N. Soave, Multiple normalized solutions for a competing system of Schrödinger equations. Calc. Var. Partial Differential Equations, 58 (1): 58:22, 2019. Doi: 10.1007/s00526-018-1476-x. Link

23) N. Soave and T. Weth, The unique continuation property of sublinear equations. SIAM Journal of Mathematical Analysis, 50 (4): 3919--3938, 2018. Doi: 10.1137/17M1144325. Link

22) N. Soave and S. Terracini. The nodal set of solutions to some elliptic problems: sublinear equations, and unstable two-phase membrane problem. Advances in Mathematics, 334: 243--299, 2018. Doi: 10.1016/j.aim.2018.06.007. Link

21) N. Soave, H. Tavares, S. Terracini and A. Zilio, Variational problems with long-range interaction. Archive for Rational Mechanics and Analysis, 228 (3): 743--772, 2018. Doi: 10.1007/s00205-017-1204-2 Link

20) S. Dipierro, N. Soave and E. Valdinoci, On stable solutions of boundary reaction-diffusion equations and applications to nonlocal problems with Neumann data. Indiana University Mathematical Journal, 67 (1): 429--469, 2018. Doi: 10.1512/iumj.2018.67.6282   Link

19) A. Pistoia and N. Soave, On Coron's problem for weakly coupled elliptic systems. Proceedings of the London Mathematical Society, 116 (1): 33--67, 2018. Doi: 10.1112/plms.12073 Link

18) S. Dipierro, N. Soave and E. Valdinoci, On fractional elliptic equations in Lipschitz sets and epigraphs: regularity, monotonicity and rigidity results. Mathematische Annalen, 369 (3-4): 1283--1326, 2017. Doi: 10.1007/s00208-016-1487-x Link

17) T. Bartsch and N. Soave, A natural constraint approach to normalized solutions of nonlinear Schrödinger equations and systems. Journal of Functional Analysis. 272 (12): 4998--5037, 2017. Doi: 10.1016/j.jfa.2017.01.025 Link 

See also Correction to: "A natural constraint approach to normalized solutions of nonlinear Schrödinger equations and systems'' [J. Funct. Anal. 272 (12) (2017) 4998–5037]. Journal of Functional Analysis, 275(2): 516--521, 2018. Link

16) N. Soave and A. Zilio, On phase separation in systems of coupled elliptic equations: asymptotic analysis and geometric aspects. Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire, 34 (3): 625--654, 2017. Doi: 10.1016/j.anihpc.2016.04.001 Link

15) T. Bartsch, L. Jeanjean and N. Soave, Normalized solutions for a system of coupled cubic Schrödinger equations on R^3. Journal de Mathématiques Pures et Appliquées, 106 (4): 583--614, 2016. Doi: 10.1016/j.matpur.2016.03.004. Link

14) N. Soave and A. Zilio, Multidimensional entire solutions for an elliptic system modelling phase separation. Analysis and Partial Differential Equations, 9 (5): 1019--1041, 2016. Doi: 10.2140/apde.2016.9.1019 Link

13) N. Soave and H. Tavares, New existence and symmetry results for least energy positive solutions of Schrödinger systems with mixed cooperation and competition terms. Journal of Differential Equations, 261: 505--537, 2016. Doi: 10.1016/j.jde.2016.03.015 Link

12) N. Soave, H. Tavares, S. Terracini and A. Zilio, Hölder bounds and regularity of emerging free boundaries for strongly competing Schrödinger equations with nontrivial grouping. Nonlinear Analysis: Theory, Methods & Applications, 138: 388--427, 2016.

Special Volume in honor of Juan Luis Vázquez for his 70th birthday. Doi: 10.1016/j.na.2015.10.023 Link  

11) N. Soave and A. Zilio, Uniform bounds for strongly competing systems: the optimal Lipschitz case. Archive Ration. Mech. Anal., 218: 647--697, 2015. Doi: 10.1007/s00205-015-0867-9 Link

10) N. Soave and S. Terracini, Liouville theorems and 1-dimensional symmetry for solutions of an elliptic system modelling phase-separation. Advances in Math., 279, 29--66, 2015. Doi: 10.1016/j.aim.2015.03.015. Link

9) N. Soave, On existence and phase separation of solitary waves for nonlinear Schrödinger systems modelling simultaneous cooperation and competition. Calc. Var. Partial Differential Equations, 53 (3-4): 689--718, 2015. Doi: 10.1007/s00526-014-0764-3. Link

8) N. Soave, Symbolic dynamics: from the N-centre to the (N+1)-body problem, a preliminary study, NoDEA Nonlin. Differential Equations and Appl., 21 (3): 371--413, 2014. Doi: 10.1007/s00030-013-0251-0 Link

7) A. Farina and N. Soave, Monotonicity and 1-dimensional symmetry for solutions of an elliptic system arising in Bose-Einstein condensation, Archive Ration. Mech. Anal., 213 (1): 287--326, 2014. Doi: 10.1007/s00205-014-0724-2 Link

6)  N. Soave and G. Verzini, Bounded solutions for a forced bounded oscillator without friction, J. Differential Equations, 256 (7): 2526--2558, 2014. Doi: 10.1016/j.jde.2014.01.015 Link

5)  N. Soave and A. Zilio, Entire solutions with exponential growth for an elliptic system modeling phase-separation, Nonlinearity, 27 (2): 305--342, 2014. Doi: 10.1088/0951-7715/27/2/305 Link

4) N. Soave and S. Terracini, Avoiding collisions under topological constraints in variational problems coming from celestial mechanics, J. Fixed Point Theory and Appl., 14 (2): 457--501, 2013.

Special Volume The Yvonne Choquet-Bruhat Festschrift. Doi: 10.1007/s11784-014-0174-3 Link

3) A. Farina and N. Soave, Symmetry and uniqueness of nonnegative solutions of some problems in the half-space, Journal of Math. Anal. Appl., 403 (1): 215--233, 2013. Doi: 10.1016/j.jmaa.2013.02.048 Link

2) N. Soave and S. Terracini, Symbolic dynamics for the N-centre problem at negative energies, Discrete Contin. Dynam. Syst. - Series A, 32 (9): 3245--3301, 2012.

Special Volume Orlando Issue Contributed by the Plenary Speakers. Doi: 10.3934/dcds.2012.32.3245 Link

See also Addendum to: symbolic dynamics for the N-centre problem at negative energies, 33 (8), 2013.

1) A. Capietto and N. Soave, Some remarks on Mather's theorem and Aubry-Mather sets, Comm. Applied Analysis, 15: 283--298, 2011. Link

PhD Thesis: