Uniqueness and rigidity in nonlinear elliptic equations, interpolation inequalities, and spectral estimates

DOI10.5802/afst.1557zbMath1397.35109arXiv1412.2915OpenAlexW2946756678MaRDI QIDQ4609680

Michał Kowalczyk, Jean Dolbeault

Publication date: 23 March 2018

Published in: Annales de la Faculté des sciences de Toulouse : Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.2915

zbMATH Keywords

Laplace operatorsemilinear elliptic equationLin-Ni conjectureNeumann boundary condiion

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (4)

φ-Entropies: convexity, coercivity and hypocoercivity for Fokker–Planck and kinetic Fokker–Planck equations ⋮ Keller-Lieb-Thirring inequalities for Schrödinger operators on cylinders ⋮ A Paneitz-Branson type equation with Neumann boundary conditions ⋮ Interpolation inequalities in \(\text{W}^{1,p}(\mathbb{S}^1)\) and \textit{carré du champ} methods

Cites Work

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• Spectral properties of Schrödinger operators on compact manifolds: rigidity, flows, interpolation and spectral estimates
• Keller-Lieb-Thirring inequalities for Schrödinger operators on cylinders
• Radial symmetry and symmetry breaking for some interpolation inequalities
• Global branch from the second eigenvalue for a semilinear Neumann problem in a ball
• On the Bakry-Emery criterion for linear diffusions and weighted porous media equations
• Uniqueness for the solution of semi-linear elliptic Neumann problems in \({\mathbb{R}}^3\)
• Asymptotic behaviors of a class of \(N\)-Laplacian Neumann problems with large diffusion
• Global branches of non-radially symmetric solutions to a semilinear Neumann problem in a disk
• The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation
• Large amplitude stationary solutions to a chemotaxis system
• Global bifurcation of steady-state solutions
• Global solution branches of two point boundary value problems
• Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations
• Uniqueness results through a priori estimates. I: A three dimensional Neumann problem
• Uniqueness of positive solutions of \(\Delta u+f(u)=0\) in \(\mathbb{R}^N\), \(N\geqq 3\)
• Sobolev inequalities and Myers's diameter theorem for an abstract Markov generator
• Nodal solutions for a sublinear elliptic equation
• Sharp interpolation inequalities on the sphere: new methods and consequences
• Interpolation inequalities on the sphere: linear vs. nonlinear flows
• Nonlinear flows and rigidity results on compact manifolds
• Improved interpolation inequalities on the sphere
• Improved Gagliardo-Nirenberg-Sobolev inequalities on manifolds with positive curvature
• Interpolation between logarithmic Sobolev and Poincaré inequalities
• Uniqueness and a priori estimates for some nonlinear elliptic Neumann equations in \(\mathbb R^3\)
• Spectral estimates on the sphere
• Rigidity versus symmetry breaking via nonlinear flows on cylinders and Euclidean spaces
• One-dimensional Gagliardo-Nirenberg-Sobolev inequalities: remarks on duality and flows
• On Lin-Ni's conjecture in convex domains
• Lower Bounds and Isoperimetric Inequalities for Eigenvalues of the Schrödinger Equation
• On the Neumann Problem for Some Semilinear Elliptic Equations and Systems of Activator-Inhibitor Type
• A Generalized Poincare Inequality for Gaussian Measures
• Global and local behavior of positive solutions of nonlinear elliptic equations
• Logarithmic Sobolev Inequalities
• Semilinear Neumann boundary value problems on a rectangle
• Symmetry in an elliptic problem and the blow—up set of
• A scenario for symmetry breaking in Caffarelli–Kohn–Nirenberg inequalities
• Branches of non-symmetric critical points and symmetry breaking in nonlinear elliptic partial differential equations
• Optimal Transport
• A strong maximum principle and a compact support principle for singular elliptic inequalities

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