Some new symmetry results for elliptic problems on the sphere and in Euclidean space
type: Item
instance of: scholarly article
title: Some new symmetry results for elliptic problems on the sphere and in Euclidean space
zbMATH Open document ID: 1008.35002
DOI: 10.1007/BF02904257
publication date: 2002-12-17T00:00:00Z
review text: There are given symmetry results for positive solutions of elliptic problems in \(\mathbb{R}^n\) and on the sphere. The authors consider linear boundary value problems as well as a semilinear problem for the \(p\)-Laplacian operator and the Laplace-Beltrami operator. The techniques utilized are the moving plane method, rearrangement inequalities and stereographic projection.
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35B50
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 1846800
zbMATH Keywords: elliptic equation
zbMATH Keywords: maximum principle
zbMATH Keywords: uniqueness of the solution
zbMATH Keywords: symmetry of the solution
zbMATH Keywords: rearrangement
zbMATH Keywords: stereographic projection
author: Friedemann Brock
author: J. Prajapat
MaRDI profile type: Publication
cites work: Q4379813
cites work: Green’s function, harmonic transplantation, and best Sobolev constant in spaces of constant curvature
cites work: On the method of moving planes and the sliding method
cites work: Continuous Steiner‐Symmetrization
cites work: Continuous rearrangement and symmetry of solutions of elliptic problems
cites work: An approach to symmetrization via polarization
cites work: A symmetry result for the p-laplacian equation via the moving planes method
cites work: Some notes on the method of moving planes
cites work: Comparison theorems for some quasilinear degenerate elliptic operators and applications to symmetry and monotonicity results
cites work: Q4237649
cites work: Q3803507
cites work: On maximum principles and existence of positive solutions for some cooperative elliptic systems
cites work: A Symmetry Result Related to Some Overdetermined Boundary Value Problems
cites work: Symmetry and related properties via the maximum principle
cites work: Quasilinear elliptic equations involving critical Sobolev exponents
cites work: Existence and uniqueness of positive radial solutions for a class of quasilinear elliptic equations
cites work: Symmetry or not?
cites work: Symmetry of positive solutions of a quasilinear elliptic equation via isoperimetric inequalities
cites work: Serrin's result for hyperbolic space and sphere
cites work: Symmetry and Overdetermined Boundary Value Problems
cites work: Symmetry properties of positive solutions of elliptic equations on symmetric domains
cites work: A symmetry problem in potential theory
cites work: A strong maximum principle for some quasilinear elliptic equations
cites work: Q4038297
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 1846800