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A characterization of balls using the domain derivative. (English) Zbl 1128.35311

Summary: In this note we give a characterization of balls in \(\mathbb{R}^N\) using the domain derivative. As a byproduct we will show that an overdetermined Steklov eigenvalue problem is solvable if and only if the domain of interest is a ball.

MSC:

35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J25 Boundary value problems for second-order elliptic equations
35P05 General topics in linear spectral theory for PDEs
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