Polyharmonic equations involving surface measures

DOI10.4171/ifb/503arXiv2212.06624OpenAlexW4389762950MaRDI QIDQ6123798

Marius Müller

Publication date: 8 April 2024

Published in: Interfaces and Free Boundaries (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2212.06624

zbMATH Keywords

signed distance functionpolyharmonic equationsPDEs with measuresAlt-Caffarelli problem

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Applications of operator theory in the physical sciences (47N50) Higher-order elliptic equations (35J30) PDEs with measure (35R06)

Cites Work

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• Elliptic PDEs, measures and capacities. From the Poisson equation to nonlinear Thomas-Fermi problems
• Polyharmonic boundary value problems. Positivity preserving and nonlinear higher order elliptic equations in bounded domains
• Existence theorem for a minimum problem with free discontinuity set
• A free boundary problem driven by the biharmonic operator
• The biharmonic Alt-Caffarelli problem in 2D
• Limit behaviour of a singular perturbation problem for the biharmonic operator
• Approximation of domains with Lipschitzian boundary