On the regularity of minima of non-autonomous functionals
<p style="text-align:justify;"> We consider regularity issues for minima of non-autonomous functionals in the Calculus of Variations exhibiting non-uniform ellipticity features. We provide a few sharp regularity results for local minimizers that also cover the case of functionals wi...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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Springer
2019
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| _version_ | 1797090348101533696 |
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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 | <p style="text-align:justify;"> We consider regularity issues for minima of non-autonomous functionals in the Calculus of Variations exhibiting non-uniform ellipticity features. We provide a few sharp regularity results for local minimizers that also cover the case of functionals with nearly linear growth. The analysis is carried out provided certain necessary approximation-in-energy conditions are satisfied. These are related to the occurrence of the so-called Lavrentiev phenomenon that non-autonomous functionals might exhibit, and which is a natural obstruction to regularity. In the case of vector valued problems, we concentrate on higher gradient integrability of minima. Instead, in the scalar case, we prove local Lipschitz estimates. We also present an approach via a variant of Moser’s iteration technique that allows to reduce the analysis of several non-uniformly elliptic problems to that for uniformly elliptic ones.</p> |
| first_indexed | 2024-03-07T03:17:16Z |
| format | Journal article |
| id | oxford-uuid:b63a9101-5b13-46bb-804a-05e7f03d3fdd |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:17:16Z |
| publishDate | 2019 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:b63a9101-5b13-46bb-804a-05e7f03d3fdd2022-03-27T04:39:25ZOn the regularity of minima of non-autonomous functionalsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:b63a9101-5b13-46bb-804a-05e7f03d3fddEnglishSymplectic Elements at OxfordSpringer2019De Filippis, CMingione, G <p style="text-align:justify;"> We consider regularity issues for minima of non-autonomous functionals in the Calculus of Variations exhibiting non-uniform ellipticity features. We provide a few sharp regularity results for local minimizers that also cover the case of functionals with nearly linear growth. The analysis is carried out provided certain necessary approximation-in-energy conditions are satisfied. These are related to the occurrence of the so-called Lavrentiev phenomenon that non-autonomous functionals might exhibit, and which is a natural obstruction to regularity. In the case of vector valued problems, we concentrate on higher gradient integrability of minima. Instead, in the scalar case, we prove local Lipschitz estimates. We also present an approach via a variant of Moser’s iteration technique that allows to reduce the analysis of several non-uniformly elliptic problems to that for uniformly elliptic ones.</p> |
| spellingShingle | De Filippis, C Mingione, G On the regularity of minima of non-autonomous functionals |
| title | On the regularity of minima of non-autonomous functionals |
| title_full | On the regularity of minima of non-autonomous functionals |
| title_fullStr | On the regularity of minima of non-autonomous functionals |
| title_full_unstemmed | On the regularity of minima of non-autonomous functionals |
| title_short | On the regularity of minima of non-autonomous functionals |
| title_sort | on the regularity of minima of non autonomous functionals |
| work_keys_str_mv | AT defilippisc ontheregularityofminimaofnonautonomousfunctionals AT mingioneg ontheregularityofminimaofnonautonomousfunctionals |