Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations
type: Item
instance of: scholarly article
title: Monotonicity, symmetry and antisymmetry of solutions of semilinear elliptic equations
zbMATH Open document ID: 0698.35031
DOI: 10.1016/0393-0440(88)90006-X
author: Henri Berestycki
author: Louis Nirenberg
published in: Journal of Geometry and Physics
publication date: 1988-01-01T00:00:00Z
review text: This paper is concerned with various qualitative properties of solutions of semilinear or quasilinear second order elliptic equations. These properties include symmetry, antisymmetry and monotonicity properties. Proofs rely upon the so-called moving planes method and involve various extensions or variants of the work by B. Gidas, W. M. Ni and L. Nirenberg.
Mathematics Subject Classification ID: 35B99
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35B50
zbMATH DE Number: 4144479
zbMATH Keywords: semilinear
zbMATH Keywords: quasilinear
zbMATH Keywords: symmetry
zbMATH Keywords: antisymmetry
zbMATH Keywords: monotonicity
zbMATH Keywords: moving planes method
MaRDI profile type: Publication
cites work: The uniqueness of Hill's spherical vortex
cites work: Q5548618
cites work: Symmetry and related properties via the maximum principle
cites work: Q3923023
cites work: A Remark on Bony Maximum Principle
cites work: Q3342966
cites work: A symmetry problem in potential theory
cites work: A Counterexample to the Nodal Domain Conjecture and a Related Semilinear Equation
Recommended article: Symmetry And Monotonicity Properties For Positive Solutions Of Semi-Linear Elliptic PDE'S
Recommended article: Q4354891
Recommended article: Symmetry and monotonicity for systems of semilinear elliptic equations in a half space
Recommended article: Monotonicity and Symmetry of Solutions of Fully Nonlinear Elliptic Equations on Bounded domains
Recommended article: Monotonicity and symmetry of solutions of elliptic systems in general domains
Recommended article: Monotonicity and symmetry of solutions of fully nonlinear elliptic equations on unbounded domains
Recommended article: Symmetry and monotonicity results for solutions of semilinear PDEs in sector-like domains
Recommended article: Q2764208
Recommended article: Monotonicity and symmetry of singular solutions to quasilinear problems
Recommended article: Monotonicity and symmetry results for \(p\)-Laplace equations and applications
description: scientific article; zbMATH DE number 4144479