A Riemannian Point of View for a Quadrature Surface Free Boundary Problem

DOI10.1007/978-3-031-04616-2_14OpenAlexW4313018604MaRDI QIDQ6186878

Diaraf Seck, Unnamed Author

Publication date: 5 February 2024

Published in: Trends in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-031-04616-2_14

zbMATH Keywords

PDEmaximum principleshape optimizationfree boundaryquadrature surface\(N\)-dimensional Riemannian manifold

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Elliptic equations on manifolds, general theory (58J05) Free boundary problems for PDEs (35R35) PDEs on manifolds (35R01) Overdetermined boundary value problems for PDEs and systems of PDEs (35N25)

Cites Work

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• Symmetry and related properties via the maximum principle
• Existence of quadrature surfaces for positive measures with finite support
• Subsolutions and supersolutions in a free boundary problem
• Shape variation and optimization. A geometrical analysis
• An existence result for a quadrature surface free boundary problem
• Quadrature surfaces as free boundaries
• Some geometric properties for a class of non-Lipschitz domains
• New extremal domains for the first eigenvalue of the Laplacian in flat tori
• A symmetry problem in potential theory
• Shapes and Geometries

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