Geometric properties of superlevel sets of semilinear elliptic equations in convex domains

DOI10.1007/978-3-030-38230-8_16zbMath1441.35123OpenAlexW3015435499MaRDI QIDQ5118799

Yannick Sire, François Hamel, Nikolai S. Nadirashvili

Publication date: 27 August 2020

Published in: 2018 MATRIX Annals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-38230-8_16

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Maximum principles in context of PDEs (35B50) Nonlinear elliptic equations (35J60)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Critical points of solutions to quasilinear elliptic problems
• Convexity of level curves for an initial value problem
• Is quasi-concavity preserved by heat flow?
• Liouville-type results for semilinear elliptic equations in unbounded domains
• Extremality conditions for the quasi-concavity function and applications
• Rearrangements and convexity of level sets in PDE
• Convexity of solutions of semilinear elliptic equations
• Convex solutions of certain elliptic equations have constant rank Hessians
• Stable solutions of semilinear elliptic problems in convex domains
• Symmetry and related properties via the maximum principle
• Le nombre de solutions de certains problèmes semi-linéaires elliptiques
• Extension of two theorems of Payne to some nonlinear Dirichlet problems
• Uniqueness of least energy solutions to a semilinear elliptic equation in \(\mathbb{R}^ 2\)
• Convex viscosity solutions and state constraints
• 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
• On two conjectures in the fixed membrane eigenvalue problem
• Removable singularities for linear parabolic equations
• Analysis of the periodically fragmented environment model. I: Species persistence
• Convexity of level sets for elliptic problems in convex domains or convex rings: Two counterexamples
• A constant rank theorem for quasiconcave solutions of fully nonlinear partial differential equations
• Convexity of Solutions to Some Elliptic Partial Differential Equations
• The power concavity of solutions of some semilinear elliptic boundary-value problems
• A Result Concerning Convex Level Surfaces of 3-Dimensional Harmonic Functions
• When are solutions to nonlinear elliptic boundary value problems convex?
• Two geometrical properties of solutions of semilinear problems
• The principal eigenvalue and maximum principle for second‐order elliptic operators in general domains
• On the uniqueness, monotonicity, starlikeness, and convexity of solutions for a nonlinear boundary value problem in elliptic PDEs
• Quasi–concave envelope of a function and convexity of level sets of solutions to elliptic equations
• Non-convexity of level sets in convex rings for semilinear elliptic problems
• A remark on N. Korevaar's concavity maximum principle and on the asymptotic uniqueness of solutions to the plasma problem
• Convexity properties of solutions to some classical variational problems
• ON THE SHAPE OF THE SOLUTIONS OF SOME SEMILINEAR ELLIPTIC PROBLEMS
• Strict convexity of level sets of solutions of some nonlinear elliptic equations
• Conexity Of Level Sets For Solutions To elliptic Ring Problems
• Starshapedness of level sets of solutions to elliptic PDEs
• Removable singularities of solutions of elliptic equations
• Addendum

This page was built for publication: Geometric properties of superlevel sets of semilinear elliptic equations in convex domains