Journal article
Manifold constrained non-uniformly elliptic problems
- Abstract:
- We consider the problem of minimizing variational integrals defined on nonlinear Sobolev spaces of competitors taking values into the sphere. The main novelty is that the underlying energy features a non-uniformly elliptic integrand exhibiting different polynomial growth conditions and no homogeneity. We develop a few intrinsic methods aimed at proving partial regularity of minima and providing techniques for treating larger classes of similar constrained non-uniformly elliptic variational problems. To give estimates for the singular sets, we use a general family of Hausdorff type measures following the local geometry of the integrand. A suitable comparison is provided with respect to the naturally associated capacities.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, pdf, 363.4KB, Terms of use)
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- Publisher copy:
- 10.1007/s12220-019-00275-3
Authors
- Publisher:
- Springer
- Journal:
- Journal of Geometric Analysis More from this journal
- Volume:
- 30
- Pages:
- 1661-1723
- Publication date:
- 2019-09-20
- Acceptance date:
- 2019-09-13
- DOI:
- EISSN:
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1559-002X
- ISSN:
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1050-6926
- Language:
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English
- Keywords:
- Pubs id:
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pubs:1054617
- UUID:
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uuid:d217d120-16d7-4fcb-bf15-6f6800f71d65
- Local pid:
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pubs:1054617
- Source identifiers:
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1054617
- Deposit date:
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2019-09-21
Terms of use
- Copyright holder:
- Mathematica Josephina, Inc.
- Copyright date:
- 2019
- Rights statement:
- © Mathematica Josephina, Inc. 2019.
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from Springer at: https://doi.org/10.1007/s12220-019-00275-3
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