Inhomogeneous global minimizers to the one-phase free boundary problem

DOI10.1080/03605302.2022.2051187zbMath1491.35134arXiv2106.14576OpenAlexW3176505245MaRDI QIDQ5864720

Daniela De Silva, David S. Jerison, Henrik Shahgholian

Publication date: 8 June 2022

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2106.14576

zbMATH Keywords

energy functionalminimizersLaplace equationfree boundaryinhomogeneous solutions

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Free boundary problems for PDEs (35R35) Variational methods for second-order elliptic equations (35J20)

Related Items

Graphical solutions to one-phase free boundary problems, The symmetric (log-)epiperimetric inequality and a decay-growth estimate

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• An overdetermined problem in potential theory
• Some remarks on stability of cones for the one-phase free boundary problem
• A Harnack inequality approach to the regularity of free boundaries. I: Lipschitz free boundaries are \(C^{1,\alpha}\)
• Partial regularity for a minimum problem with free boundary
• On an overdetermined elliptic problem
• Classification of the solutions to an overdetermined elliptic problem in the plane
• A singular energy minimizing free boundary
• Area minimizing hypersurfaces with isolated singularities.
• Local Estimates for Subsolutions and Supersolutions of Oblique Derivative Problems for General Second Order Elliptic Equations
• A Harnack inequality approach to the regularity of free boundaries part II: Flat free boundaries are Lipschitz
• Structure of One-Phase Free Boundaries in the Plane
• Global energy minimizers for free boundary problems and full regularity in three dimensions
• Oblique Derivative Problems for Elliptic Equations
• The singular homogeneous solutions to one phase free boundary problem