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Regularity of minimizers of the area functional in metric spaces
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Published/Copyright:
February 25, 2014
Abstract
In this article we study minimizers of functionals of linear growth in metric measure spaces. We introduce the generalized problem in this setting, and prove existence and local boundedness of the minimizers. We give counterexamples to show that in general, minimizers are not continuous and can have jump discontinuities inside the domain.
Funding source: Academy of Finland
Funding source: Väisälä Foundation
Received: 2013-9-25
Revised: 2014-2-3
Accepted: 2014-2-11
Published Online: 2014-2-25
Published in Print: 2015-1-1
© 2015 by De Gruyter
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- Frontmatter
- Bi-Sobolev homeomorphism with zero minors almost everywhere
- Fine properties of the subdifferential for a class of one-homogeneous functionals
- Quasiconvexity equals lamination convexity for isotropic sets of 2 × 2 matrices
- Regularity of minimizers of the area functional in metric spaces
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Articles in the same Issue
- Frontmatter
- Bi-Sobolev homeomorphism with zero minors almost everywhere
- Fine properties of the subdifferential for a class of one-homogeneous functionals
- Quasiconvexity equals lamination convexity for isotropic sets of 2 × 2 matrices
- Regularity of minimizers of the area functional in metric spaces
- On the relaxation of variational integrals in metric Sobolev spaces
