Work

Continuity up to the boundary for minimizers of the one-phase Bernoulli problem

Year: 2025

Type: article

Abstract: We prove new boundary regularity results for minimizers to the one-phase Alt-Caffarelli functional (also known as Bernoulli free boundary problem) in the case of continuous and Hölder-continuous boundary data. As an application, we use them to extend recent generic uniqueness and regularity results to families of continuous functions.

Source: Calculus of Variations and Partial Differential Equations

DOI: 10.1007/s00526-025-03040-3

Authors: Xavier Fernández-Real, Florian Gruen

Institutions: École Polytechnique Fédérale de Lausanne, Kyoto University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190