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:
3) N. Soave and S. Terracini. On partially segregated harmonic maps: optimal regularity and struc- ture of the free boundary. Preprint arXiv 2024.
2) N. Soave and S. Terracini. On some singularly perturbed elliptic systems modeling partial seg- regation: uniform Hölder estimates and basic properties of the limits. Preprint arXiv 2024.
1) L. Pollastro and N. Soave. Antisymmetric maximum principles and Hopf ’s lemmas for the Log- arithmic Laplacian, with applications to symmetry results. Preprint arXiv 2024.
Publications on international journals:
44) F. Esposito, B. Sciunzi and N. Soave. Notes on overdetermined singular problems. Bulletin of the London Mathematical Society, 56(4): 1341–1350, 2024. Doi: 10.1112/blms.12996. Link
43) S. Dipierro, N. Soave and E. Valdinoci. A fractional Hopf Lemma for sign-changing solutions. Communications in Partial Differential Equations, 49(3), 217–241, 2024. Doi: 10.1080/03605302.2024.2337637. Link
42) M. Muratori and N. Soave. Radial solutions of the Lane-Emden system on Cartan-Hadamard manifolds: asymptotics and rigidity. International Mathematics Research Notices, 12: 9910–9935, 2024. Doi: 10.1093/imrn/rnae079. Link
41) J. Borthwick, X. Chang, L. Jeanjean and N. Soave. Bounded Palais-Smale sequences with Morse-type information for some constrained functionals. Transactions of the American Mathematical Society, 377(6): 4481–4517, 2024. Doi: 10.1090/tran/9145. Link
40) N. Soave and G. Tortone. On the nodal set of solutions to some sublinear equations without homogeneity. Archive for Rational Mechanics and Analysis, 248(2), Paper No. 26, 33 p., 2024. Doi: 10.1007/s00205-024-01970-4. Link
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:
Variational and geometric methods for nonlinear differential equations. Link