Higher integrability for constrained minimizers of integral functionals with (p, q)-growth in low dimension
We prove higher summability for the gradient of minimizers of strongly convex integral functionals of the Calculus of Variations ˆ Ω f(x, Du(x)) dx, u : Ω ⊂ R n → S N−1 , with growth conditions of (p, q)-type: |ξ| p ≤ f(x, ξ) ≤ C(|ξ| q + 1), p < q, in low dimension. Our procedure is set in th...
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| Format: | Journal article |
| Language: | English |
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Elsevier
2018
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| _version_ | 1797062597535596544 |
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| author | De Filippis, C |
| author_facet | De Filippis, C |
| author_sort | De Filippis, C |
| collection | OXFORD |
| description | We prove higher summability for the gradient of minimizers of strongly convex integral functionals of the Calculus of Variations ˆ Ω f(x, Du(x)) dx, u : Ω ⊂ R n → S N−1 , with growth conditions of (p, q)-type: |ξ| p ≤ f(x, ξ) ≤ C(|ξ| q + 1), p < q, in low dimension. Our procedure is set in the framework of Fractional Sobolev Spaces and renders the desired regularity as the result of an approximation technique relying on estimates obtained through a careful use of difference quotients. |
| first_indexed | 2024-03-06T20:47:48Z |
| format | Journal article |
| id | oxford-uuid:368246ff-63f0-434e-bc3c-bae64ec3686c |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T20:47:48Z |
| publishDate | 2018 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:368246ff-63f0-434e-bc3c-bae64ec3686c2022-03-26T13:38:23ZHigher integrability for constrained minimizers of integral functionals with (p, q)-growth in low dimensionJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:368246ff-63f0-434e-bc3c-bae64ec3686cEnglishSymplectic Elements at OxfordElsevier2018De Filippis, CWe prove higher summability for the gradient of minimizers of strongly convex integral functionals of the Calculus of Variations ˆ Ω f(x, Du(x)) dx, u : Ω ⊂ R n → S N−1 , with growth conditions of (p, q)-type: |ξ| p ≤ f(x, ξ) ≤ C(|ξ| q + 1), p < q, in low dimension. Our procedure is set in the framework of Fractional Sobolev Spaces and renders the desired regularity as the result of an approximation technique relying on estimates obtained through a careful use of difference quotients. |
| spellingShingle | De Filippis, C Higher integrability for constrained minimizers of integral functionals with (p, q)-growth in low dimension |
| title | Higher integrability for constrained minimizers of integral functionals with (p, q)-growth in low dimension |
| title_full | Higher integrability for constrained minimizers of integral functionals with (p, q)-growth in low dimension |
| title_fullStr | Higher integrability for constrained minimizers of integral functionals with (p, q)-growth in low dimension |
| title_full_unstemmed | Higher integrability for constrained minimizers of integral functionals with (p, q)-growth in low dimension |
| title_short | Higher integrability for constrained minimizers of integral functionals with (p, q)-growth in low dimension |
| title_sort | higher integrability for constrained minimizers of integral functionals with p q growth in low dimension |
| work_keys_str_mv | AT defilippisc higherintegrabilityforconstrainedminimizersofintegralfunctionalswithpqgrowthinlowdimension |