Regularity for quasi-minima of the Alt–Caffarelli functional

We investigate regularity estimates of quasi-minima of the Alt–Caffarelli energy functional. We prove universal Hölder continuity of quasi-minima and optimal Lipchitz regularity along their free boundaries.

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2024-07, Vol.63 (6), Article 149
Main Authors: Pellegrino, Daniel M., Teixeira, Eduardo V.
Format: Article
Language:English
Subjects:
Analysis
Calculus of Variations and Optimal Control
Optimization
Continuity (mathematics)
Control
Free boundaries
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Regularity
Systems Theory
Theoretical
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Description
Summary:We investigate regularity estimates of quasi-minima of the Alt–Caffarelli energy functional. We prove universal Hölder continuity of quasi-minima and optimal Lipchitz regularity along their free boundaries.
ISSN:0944-2669
1432-0835
DOI:10.1007/s00526-024-02773-x