Molzon, Robert Symmetry and overdetermined boundary value problems. (English) Zbl 0789.35118 Forum Math. 3, No. 2, 143-156 (1991). Summary: A polarized version of Bochner’s identity is used to obtain symmetry results for an overdetermined boundary value problem on constant curvature manifolds. The identity is also used to prove a Rellich identity for Dirichlet eigenvalues of the Laplacian. Finally, a reflection argument which was developed by Alexandrov is used to obtain symmetry results for overdetermined boundary value problems on constant curvature manifolds. Cited in 1 ReviewCited in 24 Documents MSC: 35N05 Overdetermined systems of PDEs with constant coefficients 53C20 Global Riemannian geometry, including pinching 31C12 Potential theory on Riemannian manifolds and other spaces 58J05 Elliptic equations on manifolds, general theory Keywords:Bochner’s identity; overdetermined boundary value problem on constant curvature manifolds; Rellich identity for Dirichlet eigenvalues of the Laplacian; symmetry results PDFBibTeX XMLCite \textit{R. Molzon}, Forum Math. 3, No. 2, 143--156 (1991; Zbl 0789.35118) Full Text: DOI EuDML