Higher differentiability of minimizers of convex variational integrals
In this paper we consider integral functionals of the formF(v,Ω)= ∫ΩF(Dv(x))dx with convex integrand satisfying (p,q) growth conditions. We prove local higher differentiability results for bounded minimizers of the functional F under dimension-free conditions on the gap between the growth and the co...
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| Format: | Journal article |
| Language: | English |
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2011
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| _version_ | 1826275338024386560 |
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| author | Carozza, M Kristensen, J di Napoli, A |
| author_facet | Carozza, M Kristensen, J di Napoli, A |
| author_sort | Carozza, M |
| collection | OXFORD |
| description | In this paper we consider integral functionals of the formF(v,Ω)= ∫ΩF(Dv(x))dx with convex integrand satisfying (p,q) growth conditions. We prove local higher differentiability results for bounded minimizers of the functional F under dimension-free conditions on the gap between the growth and the coercivity exponents. As a novel feature, the main results are achieved through uniform higher differentiability estimates for solutions to a class of auxiliary problems, constructed adding singular higher order perturbations to the integrand. © 2011 Elsevier Masson SAS. All rights reserved. |
| first_indexed | 2024-03-06T22:57:12Z |
| format | Journal article |
| id | oxford-uuid:60d415b7-22f0-4914-abf8-797291887093 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T22:57:12Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:60d415b7-22f0-4914-abf8-7972918870932022-03-26T17:55:44ZHigher differentiability of minimizers of convex variational integralsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:60d415b7-22f0-4914-abf8-797291887093EnglishSymplectic Elements at Oxford2011Carozza, MKristensen, Jdi Napoli, AIn this paper we consider integral functionals of the formF(v,Ω)= ∫ΩF(Dv(x))dx with convex integrand satisfying (p,q) growth conditions. We prove local higher differentiability results for bounded minimizers of the functional F under dimension-free conditions on the gap between the growth and the coercivity exponents. As a novel feature, the main results are achieved through uniform higher differentiability estimates for solutions to a class of auxiliary problems, constructed adding singular higher order perturbations to the integrand. © 2011 Elsevier Masson SAS. All rights reserved. |
| spellingShingle | Carozza, M Kristensen, J di Napoli, A Higher differentiability of minimizers of convex variational integrals |
| title | Higher differentiability of minimizers of convex variational integrals |
| title_full | Higher differentiability of minimizers of convex variational integrals |
| title_fullStr | Higher differentiability of minimizers of convex variational integrals |
| title_full_unstemmed | Higher differentiability of minimizers of convex variational integrals |
| title_short | Higher differentiability of minimizers of convex variational integrals |
| title_sort | higher differentiability of minimizers of convex variational integrals |
| work_keys_str_mv | AT carozzam higherdifferentiabilityofminimizersofconvexvariationalintegrals AT kristensenj higherdifferentiabilityofminimizersofconvexvariationalintegrals AT dinapolia higherdifferentiabilityofminimizersofconvexvariationalintegrals |