Uniqueness of the critical point for semi-stable solutions in \(\mathbb{R}^2\)

DOI10.1007/s00526-020-01903-5zbMath1459.35212arXiv2004.11330OpenAlexW3122905706WikidataQ115386868 ScholiaQ115386868MaRDI QIDQ2225908

Massimo Grossi, Fabio De Regibus, Debangana Mukherjee

Publication date: 11 February 2021

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.11330

zbMATH Keywords

uniquenesscurvaturecritical pointsemilinear problem with Laplacian

Mathematics Subject Classification ID

Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (5)

On the number of critical points of the second eigenfunction of the Laplacian in convex planar domains ⋮ Critical points of solutions to a kind of linear elliptic equations in multiply connected domains ⋮ On the number of critical points of stable solutions in bounded strip-like domains ⋮ Towards the optimality of the ball for the Rayleigh conjecture concerning the clamped plate ⋮ On the number of critical points of solutions of semilinear elliptic equations

Cites Work

• Stable solutions of semilinear elliptic problems in convex domains
• Symmetry and related properties via the maximum principle
• On extensions of the Brunn-Minkowski and Prekopa-Leindler theorems, including inequalities for log concave functions, and with an application to the diffusion equation
• On the convexity of level lines of the fundamental mode in the clamped membrane problem, and the existence of convex solutions in a related free boundary problem
• Some Results for the Gelfand's Problem
• ON THE SHAPE OF THE SOLUTIONS OF SOME SEMILINEAR ELLIPTIC PROBLEMS
• Strict convexity of level sets of solutions of some nonlinear elliptic equations

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