## 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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