Manifold constrained non-uniformly elliptic problems
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 homogeneit...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Springer
2019
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| _version_ | 1797096475979677696 |
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| author | De Filippis, C Mingione, G |
| author_facet | De Filippis, C Mingione, G |
| author_sort | De Filippis, C |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T04:42:23Z |
| format | Journal article |
| id | oxford-uuid:d217d120-16d7-4fcb-bf15-6f6800f71d65 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T04:42:23Z |
| publishDate | 2019 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:d217d120-16d7-4fcb-bf15-6f6800f71d652022-03-27T08:01:25ZManifold constrained non-uniformly elliptic problemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:d217d120-16d7-4fcb-bf15-6f6800f71d65EnglishSymplectic Elements at OxfordSpringer2019De Filippis, CMingione, GWe 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. |
| spellingShingle | De Filippis, C Mingione, G Manifold constrained non-uniformly elliptic problems |
| title | Manifold constrained non-uniformly elliptic problems |
| title_full | Manifold constrained non-uniformly elliptic problems |
| title_fullStr | Manifold constrained non-uniformly elliptic problems |
| title_full_unstemmed | Manifold constrained non-uniformly elliptic problems |
| title_short | Manifold constrained non-uniformly elliptic problems |
| title_sort | manifold constrained non uniformly elliptic problems |
| work_keys_str_mv | AT defilippisc manifoldconstrainednonuniformlyellipticproblems AT mingioneg manifoldconstrainednonuniformlyellipticproblems |