A symmetry problem from probability. (English) Zbl 0883.35031

Summary: We examine solutions of two related boundary value problems for smooth domains in Euclidean space which arise from variational problems in probability. We show that the existence of solutions to each problem implies that the domain is a sphere.


35J40 Boundary value problems for higher-order elliptic equations
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
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