Wu, Tsung-Fang Symmetry and concentration behavior of ground state in axially symmetric domains. (English) Zbl 1129.35409 Abstr. Appl. Anal. 2004, No. 12, 1019-1030 (2004). Summary: Let \(\Omega(r)\) be axially symmetric bounded domains which satisfy some suitable conditions. Then the ground-state solutions of a semilinear elliptic equation in \(\Omega(r)\) are, in general, nonaxially symmetric and concentrated on one side. We prove a necessary and sufficient condition for the symmetry of ground-state solutions. MSC: 35J60 Nonlinear elliptic equations 35A30 Geometric theory, characteristics, transformations in context of PDEs 35J20 Variational methods for second-order elliptic equations 47J30 Variational methods involving nonlinear operators PDFBibTeX XMLCite \textit{T.-F. Wu}, Abstr. Appl. Anal. 2004, No. 12, 1019--1030 (2004; Zbl 1129.35409) Full Text: DOI EuDML