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Nonsymmetric ground states of symmetric variational problems
Author(s) -
Esteban Maria J.
Publication year - 1991
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160440205
Subject(s) - mathematics , invariant (physics) , minification , mathematical analysis , boundary value problem , domain (mathematical analysis) , symmetry (geometry) , neumann boundary condition , euler's formula , mathematical physics , geometry , mathematical optimization
Abstract In this paper we study a minimization problem which is invariant by rotation. The corresponding Euler‐Lagrange equations are semilinear elliptic equations in an exterior domain with Neumann boundary conditions. We prove that this minimization problem has at least one solution. Yet all its solutions are shown not to be rotationally invariant. Furthermore we describe how the radial symmetry is broken.