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Archive for Rational Mechanics and Analysis

, Volume 148, Issue 4, pp 265–290 | Cite as

Symmetry of Ground States of Quasilinear Elliptic Equations

  • James Serrin
  • Henghui Zou
Article

Abstract

. We consider the problem of radial symmetry for non‐negative continuously differentiable weak solutions of elliptic equations of the form \( {\rm div}(A(\vert Du\vert)Du) + f(u) = 0,\quad x\in {\vec R}^n, \quad n\geq 2,\eqno(1)\) under the ground state condition \( u(x)\to 0 \mbox{ as } \vert x\vert\to\infty. \eqno(2)\) Using the well‐known moving plane method of Alexandrov and Serrin, we show, under suitable conditions on A and f, that all ground states of (1) are radially symmetric about some origin O in \({\vec R}^n\). In particular, we obtain radial symmetry for compactly supported ground states and give sufficient conditions for the positivity of ground states in terms of the given operator A and the nonlinearity f.

Keywords

State Condition Weak Solution Elliptic Equation Suitable Condition Plane Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • James Serrin
    • 1
  • Henghui Zou
    • 2
  1. 1.Department of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USAUS
  2. 2.Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama, USAUS

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