Existence of optimal densities is proven for extremal weighted Steklov eigenvalues, with minimizers characterized as bang-bang functions possibly with disconnected support, and a Fréchet-differentiable surrogate plus numerical algorithm is introduced for computation on general domains.
Linear elliptic boundary value problems with non–smooth data: normal solvability on sobolev–campanato spaces.Mathematische Nachrichten, 225(1):39–74, 2001
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Extremal Eigenvalues of Weighted Steklov Problems
Existence of optimal densities is proven for extremal weighted Steklov eigenvalues, with minimizers characterized as bang-bang functions possibly with disconnected support, and a Fréchet-differentiable surrogate plus numerical algorithm is introduced for computation on general domains.