Topological monsters in elliptic equations and spectral theory
type: Item
instance of: scholarly article
title: Topological monsters in elliptic equations and spectral theory
zbMATH Open document ID: 1350.35009
DOI: 10.4171/EMSS/15
author: Daniel Peralta-Salas
author: Alberto Enciso
published in: EMS Surveys in Mathematical Sciences
publication date: 2016-07-14T00:00:00Z
review text: Summary: In this paper we will discuss the appearance of complicated geometric and topological structures through the level sets of solutions to a wide range of elliptic equations. Applications to the analysis of nodal sets of eigenfunctions of Schrödinger operators will be discussed too.
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35J15
Mathematics Subject Classification ID: 58J50
Mathematics Subject Classification ID: 35P05
zbMATH DE Number: 6603463
zbMATH Keywords: level sets
zbMATH Keywords: nodal sets
zbMATH Keywords: eigenfunctions of Schrödinger operators
MaRDI profile type: Publication
cites work: Q5558469
cites work: Nodal lines of eigenfunctions of the fixed membrane problem in general convex domains
cites work: Entire solutions of semilinear elliptic equations in ℝ³ and a conjecture of De Giorgi
cites work: The Topology of the Level Curves of Harmonic Functions with Critical Points
cites work: Approximation by Solutions of Partial Differential Equations
cites work: Saddle-shaped solutions of bistable diffusion equations in all of \(\mathbb R^{2m}\)
cites work: Q3961718
cites work: Sur la multiplicité de la première valeur propre non nulle du Laplacien. (On the multiplicity of the first nonzero eigenvalue of the Laplacian)
cites work: Construction de laplaciens dont une partie finie du spectre est donnée
cites work: On De Giorgi's conjecture in dimension \(N\geq 9\)
cites work: On De Giorgi’s conjecture and beyond
cites work: Entire solutions of the Allen-Cahn equation and complete embedded minimal surfaces of finite total curvature in \(\mathbb{R}^3\)
cites work: Nodal sets of eigenfunctions on Riemannian manifolds
cites work: Immersions minimales, première valeur propre du laplacien et volume conforme. (Minimal immersions, first eigenvalue of the Laplacian and conformal volume)
cites work: Laplace operators with eigenfunctions whose nodal set is a knot
cites work: Bounded solutions to the Allen-Cahn equation with level sets of any compact topology
cites work: Knots and links in steady solutions of the Euler equation
cites work: Critical points of Green's functions on complete manifolds
cites work: Submanifolds that are level sets of solutions to a second-order elliptic PDE
cites work: Existence of knotted vortex tubes in steady Euler flows
cites work: Eigenfunctions with prescribed nodal sets
cites work: Critical points and geometric properties of Green's functions on open surfaces
cites work: The Level Curves of Harmonic Functions
cites work: Closed Nodal Lines and Interior Hot Spots of the Second Eigenfunctions of the Laplacian on Surfaces
cites work: Q4719829
cites work: On a conjecture of De Giorgi and some related problems
cites work: Nodal sets for solutions of elliptic equations
cites work: Topology of Level Curves of Harmonic Functions
cites work: Symmetric Green's Functions on Complete Manifolds
cites work: A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces
cites work: Q4388960
cites work: On the nodal line of the second eigenfunction of the Laplacian in \(\mathbb{R}^ 2\)
cites work: The topology of pseudo-harmonic functions
cites work: Regularity of flat level sets in phase transitions
cites work: Generic Properties of Eigenfunctions
full work available at URL: https://doi.org/10.4171/emss/15
OpenAlex ID: W2406299997
description: scientific article; zbMATH DE number 6603463