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We study almost-minimizers of anisotropic surface energies defined by a Hölder continuous matrix of coefficients acting on the unit normal direction to the surface. In this generalization of the Plateau problem, we prove almost-minimizers are locally Hölder continuously differentiable at regular points and give dimension estimates for the size of the singular set. We work in the framework of sets of locally finite perimeter and our proof follows an excess-decay type argument.
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Free boundary regularity in the triple membrane problem
We investigate the regularity of the free boundaries in the three elastic membranes problem. We show that the two free boundaries corresponding to the coincidence regions between consecutive membranes are C1,log-hypersurfaces near a regular intersection point. We also study two types of singular intersections. The first type of singular points are locally covered by a C1,alpha-hypersurface. The second type of singular points stratify and each stratum is locally covered by a C1-manifold.
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- Award ID(s):
- 1800645
- PAR ID:
- 10407546
- Date Published:
- Journal Name:
- Ars inveniendi analytica
- Volume:
- 2021
- Issue:
- 3
- ISSN:
- 2769-8505
- Page Range / eLocation ID:
- 1-49
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
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- The DOI is not currently available.
