Some remarks on stability of cones for the one-phase free boundary problem
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Publication:496176
DOI10.1007/s00039-015-0335-6zbMath1326.49078arXiv1410.7463OpenAlexW1487567144MaRDI QIDQ496176
Ovidiu V. Savin, David S. Jerison
Publication date: 21 September 2015
Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1410.7463
smoothnessone-phase free boundary problemAlt-Caffarelli energy functionalenergy minimizing hypersurfacesstable cones
Sensitivity, stability, well-posedness (49K40) Variational problems in a geometric measure-theoretic setting (49Q20) Regularity of solutions in optimal control (49N60) Free boundary problems for PDEs (35R35)
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Cites Work
- Unnamed Item
- Unnamed Item
- 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
- Minimal varieties in Riemannian manifolds
- A gradient bound for free boundary graphs
- A singular energy minimizing free boundary
- A Harnack inequality approach to the regularity of free boundaries part II: Flat free boundaries are Lipschitz
- Global energy minimizers for free boundary problems and full regularity in three dimensions
- The singular homogeneous solutions to one phase free boundary problem
