An existence result for a quadrature surface free boundary problem. (English) Zbl 1207.35106

Summary: The aim of this paper is to present two different approaches in order to obtain an existence result to the so-called quadrature surface free boundary problem. The first one requires the shape derivative calculus while the second one depends strongly on the compatibility condition of the Neumann problem. A necessary and sufficient condition of existences is given in the radial case.


35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35A35 Theoretical approximation in context of PDEs
Full Text: DOI


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