Symmetry of positive solutions of a quasilinear elliptic equation via isoperimetric inequalities
- 1 August 1994
- journal article
- research article
- Published by Taylor & Francis in Applicable Analysis
- Vol. 54 (1-2) , 27-37
- https://doi.org/10.1080/00036819408840266
Abstract
In this paper, it is proved that positive solutions of non linear equation involving the N–Laplacian in a ball in RN with Dirichlet boundary condition are radial and radially decreasing provided that the nonlinearity is a continuous function ƒ(t) (satisfying suitable growth conditions) which is strictly positive for t>0. The method generalizes that of Lions for the Laplacian in two dimensions. The method of the present paper can also be extended to an analogous mixed boundary value problem in a convex cone.Keywords
This publication has 7 references indexed in Scilit:
- On the method of moving planes and the sliding methodBulletin of the Brazilian Mathematical Society, New Series, 1991
- On the existence of radial solutions of quasilinear elliptic equationsNonlinearity, 1990
- Isoperimetric inequalities for convex conesProceedings of the American Mathematical Society, 1990
- Symmetry properties for positive solutions of elliptic equations with mixed boundary conditionsJournal of Functional Analysis, 1989
- Quasilinear elliptic equations involving critical Sobolev exponentsNonlinear Analysis, 1989
- Two geometrical properties of solutions of semilinear problemsApplicable Analysis, 1981
- Symmetry and related properties via the maximum principleCommunications in Mathematical Physics, 1979