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.
Regularity of solutions of linear second order elliptic and parabolic boundary value problems on Lipschitz domains.Journal of Differential Equations, 251(4-5):860–880
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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.