Quadrature identities with a background PDE

DOI10.1007/s13324-022-00674-wzbMath1486.31010OpenAlexW4220957858WikidataQ114220020 ScholiaQ114220020MaRDI QIDQ2119598

Layan El Hajj, Henrik Shahgholian

Publication date: 29 March 2022

Published in: Analysis and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13324-022-00674-w

zbMATH Keywords

semilinear elliptic equationsnonlinear quadrature domains

Mathematics Subject Classification ID

Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Semilinear elliptic equations (35J61)

Cites Work

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• Characterization of balls in terms of Bessel-potential integral equation
• Characterization of balls by Riesz-potentials
• A characteristic property of spheres
• Solutions to the obstacle problem as Green potentials
• Quadrature domains
• Sharp estimates of the distance from a fixed point to the frontier of a Hele-Shaw flow
• Free boundary methods and non-scattering phenomena
• A symmetry problem in potential theory
• Shape optimization of a Dirichlet type energy for semilinear elliptic partial differential equations
• Radial symmetry for an elliptic PDE with a free boundary

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