Grossi, Massimo; Provenzano, Luigi On the critical points of semi-stable solutions on convex domains of Riemannian surfaces. (English) Zbl 07892670 Math. Ann. 389, No. 4, 3447-3470 (2024). MSC: 58J32 35J61 58J05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Mukherjee, Mayukh; Saha, Soumyajit Nodal sets of Laplace eigenfunctions under small perturbations. (English) Zbl 1495.35132 Math. Ann. 383, No. 1-2, 475-491 (2022). MSC: 35P05 35B05 35B20 35J05 58J05 58J50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
De Regibus, Fabio; Grossi, Massimo On the number of critical points of the second eigenfunction of the Laplacian in convex planar domains. (English) Zbl 1486.35311 J. Funct. Anal. 283, No. 1, Article ID 109496, 22 p. (2022). MSC: 35P05 35J25 55M25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Grossi, Massimo On the number of critical points of solutions of semilinear elliptic equations. (English) Zbl 1480.35112 Electron. Res. Arch. 29, No. 6, 4215-4228 (2021). MSC: 35J05 35J91 35J25 × Cite Format Result Cite Review PDF Full Text: DOI
Dahne, Joel; Gómez-Serrano, Javier; Hou, Kimberly A counterexample to Payne’s nodal line conjecture with few holes. (English) Zbl 1478.35154 Commun. Nonlinear Sci. Numer. Simul. 103, Article ID 105957, 13 p. (2021). MSC: 35P05 35B05 35J25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Beck, Thomas; Canzani, Yaiza; Marzuola, Jeremy L. Nodal line estimates for the second Dirichlet eigenfunction. (English) Zbl 1473.35118 J. Spectr. Theory 11, No. 1, 323-353 (2021). Reviewer: Marius Ghergu (Dublin) MSC: 35J05 35P05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Steinerberger, Stefan A spectral approach to the shortest path problem. (English) Zbl 1475.05058 Linear Algebra Appl. 620, 182-200 (2021). Reviewer: Kexiang Xu (Nanjing) MSC: 05C12 05C35 05C50 35J05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Alessandrini, Giovanni A small collection of open problems. (English) Zbl 1458.35090 Rend. Ist. Mat. Univ. Trieste 52, 591-600 (2020). MSC: 35B60 35J92 35A02 35J25 35K10 35R30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Cao, Xinlin; Diao, Huaian; Liu, Hongyu; Zou, Jun On nodal and generalized singular structures of Laplacian eigenfunctions and applications to inverse scattering problems. (English. French summary) Zbl 1452.35120 J. Math. Pures Appl. (9) 143, 116-161 (2020). Reviewer: Khanlar R. Mamedov (Mersin) MSC: 35P05 35P25 35R30 35Q60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Steinerberger, Stefan Hot spots in convex domains are in the tips (up to an inradius). (English) Zbl 1444.35034 Commun. Partial Differ. Equations 45, No. 6, 641-654 (2020). Reviewer: Andreas Kleefeld (Jülich) MSC: 35J05 60J65 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chen, Hongbin; Li, Yi; Wang, Lihe Monotone properties of the eigenfunction of Neumann problems. (English. French summary) Zbl 1425.35029 J. Math. Pures Appl. (9) 130, 112-129 (2019). MSC: 35J25 35B65 35J05 × Cite Format Result Cite Review PDF Full Text: DOI
Cheng, Xiuyuan; Rachh, Manas; Steinerberger, Stefan On the diffusion geometry of graph Laplacians and applications. (English) Zbl 1412.35353 Appl. Comput. Harmon. Anal. 46, No. 3, 674-688 (2019). MSC: 35R02 35J05 94C15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kiwan, Rola On the nodal set of a second Dirichlet eigenfunction in a doubly connected domain. (English. French summary) Zbl 1426.35173 Ann. Fac. Sci. Toulouse, Math. (6) 27, No. 4, 863-873 (2018). Reviewer: Davide Buoso (Lausanne) MSC: 35P15 35P05 35J05 49R05 × Cite Format Result Cite Review PDF Full Text: DOI
Kennedy, J. B. A toy Neumann analogue of the nodal line conjecture. (English) Zbl 1391.35291 Arch. Math. 110, No. 3, 261-271 (2018). Reviewer: Dumitru Motreanu (Juiz de Fora) MSC: 35P05 35B05 35J05 58J50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Enciso, Alberto; Peralta-Salas, Daniel Topological monsters in elliptic equations and spectral theory. (English) Zbl 1350.35009 EMS Surv. Math. Sci. 3, No. 1, 107-130 (2016). MSC: 35B05 35J15 58J50 35P05 × Cite Format Result Cite Review PDF Full Text: DOI
Lampart, Jonas Convergence of nodal sets in the adiabatic limit. (English) Zbl 1311.58017 Ann. Global Anal. Geom. 47, No. 2, 147-166 (2015). MSC: 58J50 58J32 35B05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Krejčiřík, David; Tušek, Matěj Nodal sets of thin curved layers. (English) Zbl 1323.35109 J. Differ. Equations 258, No. 2, 281-301 (2015). Reviewer: Peter B. Gilkey (Eugene) MSC: 35P05 58J50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Grossi, Massimo; Grumiau, Christopher; Pacella, Filomena Lane-Emden problems: asymptotic behavior of low energy nodal solutions. (English) Zbl 1266.35106 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 30, No. 1, 121-140 (2013). MSC: 35J91 35B40 35B32 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Donnelly, Harold Spectral gap for convex planar domains. (English) Zbl 1228.35248 Math. Z. 269, No. 1-2, 1-3 (2011). MSC: 35Q79 35K05 35J10 × Cite Format Result Cite Review PDF Full Text: DOI
Kennedy, J. B. The nodal line of the second eigenfunction of the Robin Laplacian in \(\mathbb R^2\) can be closed. (English) Zbl 1223.35242 J. Differ. Equations 251, No. 12, 3606-3624 (2011). MSC: 35P05 35B05 35J05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bonnaillie-Noël, Virginie; Helffer, Bernard; Vial, Gregory Numerical simulations for nodal domains and spectral minimal partitions. (English) Zbl 1191.35189 ESAIM, Control Optim. Calc. Var. 16, No. 1, 221-246 (2010). Reviewer: Qin Mengzhao (Beijing) MSC: 35P05 65N25 65N30 49Q10 35J05 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Grumiau, Christopher; Troestler, Christophe Nodal line structure of least energy nodal solutions for Lane-Emden problems. (English. Abridged French version) Zbl 1177.35021 C. R., Math., Acad. Sci. Paris 347, No. 13-14, 767-771 (2009). MSC: 35B05 35J65 × Cite Format Result Cite Review PDF Full Text: DOI Link
Gladiali, Francesca; Grossi, Massimo On the spectrum of a nonlinear planar problem. (English) Zbl 1166.35028 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26, No. 1, 191-222 (2009). MSC: 35P05 35P20 35P15 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Bañuelos, Rodrigo; Kulczycki, Tadeusz Eigenvalue gaps for the Cauchy process and a Poincaré inequality. (English) Zbl 1089.60029 J. Funct. Anal. 234, No. 1, 199-225 (2006). MSC: 60G52 60J45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Komendarczyk, R. On the contact geometry of nodal sets. (English) Zbl 1156.53318 Trans. Am. Math. Soc. 358, No. 6, 2399-2413 (2006). MSC: 53D10 35J05 58J50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Liboff, Richard L. Nodal and other properties of the second eigenfunction of the Laplacian in the plane. (English) Zbl 1085.65106 Q. Appl. Math. 63, No. 4, 673-679 (2005). MSC: 65N25 35P05 35J05 × Cite Format Result Cite Review PDF Full Text: DOI
Juutinen, Petri; Lindqvist, Peter On the higher eigenvalues for the \(\infty\)-eigenvalue problem. (English) Zbl 1080.35057 Calc. Var. Partial Differ. Equ. 23, No. 2, 169-192 (2005). Reviewer: Massimo Lanza de Cristoforis (Padova) MSC: 35P30 35J70 49R50 35P15 × Cite Format Result Cite Review PDF Full Text: DOI
Grossi, Massimo; Pacella, Filomena On an eigenvalue problem related to the critical exponent. (English) Zbl 1122.35087 Math. Z. 250, No. 1, 225-256 (2005). MSC: 35P15 35J65 35P10 35B33 × Cite Format Result Cite Review PDF Full Text: DOI
Bañuelos, Rodrigo; Kulczycki, Tadeusz The Cauchy process and the Steklov problem. (English) Zbl 1055.60072 J. Funct. Anal. 211, No. 2, 355-423 (2004). Reviewer: Eckhard Giere (Clausthal-Zellerfeld) MSC: 60J45 60G52 × Cite Format Result Cite Review PDF Full Text: DOI
Fournais, Søren The nodal surface of the second eigenfunction of the Laplacian in \(\mathbb{R}^D\) can be closed. (English) Zbl 1011.47033 J. Differ. Equations 173, No. 1, 145-159 (2001). Reviewer: J.Schmeelk (Richmond) MSC: 47F05 35P05 35J05 × Cite Format Result Cite Review PDF Full Text: DOI
Jerison, David; Nadirashvili, Nikolai The “hot spots” conjecture for domains with two axes of symmetry. (English) Zbl 0948.35029 J. Am. Math. Soc. 13, No. 4, 741-772 (2000). Reviewer: Vladimir Mityushev (Słupsk) MSC: 35J05 35B65 35J25 × Cite Format Result Cite Review PDF Full Text: DOI
Hoffmann-Ostenhof, M.; Hoffmann-Ostenhof, T.; Nadirashvili, N. The nodal line of the second eigenfunction of the Laplacian in \(\mathbb{R}^2\) can be closed. (English) Zbl 0956.35027 Duke Math. J. 90, No. 3, 631-640 (1997). MSC: 35J05 35B05 35P99 35B30 × Cite Format Result Cite Review PDF Full Text: DOI