{"corpus_id":36701159,"paper_sha":"1d46f16454c0d40b7811c8ec4875c10a3a82867e","doi":"10.1016/J.JDE.2009.03.018","arxiv_id":null,"pmid":null,"pmcid":null,"mag_id":2126241685,"dblp_id":null,"acl_id":null,"title":"Morrey regularity results for asymptotically convex variational problems with (p;q) growth","year":2009,"publication_date":"2009-06-15","venue":"","journal":{"name":"Journal of Differential Equations","pages":"4519-4551","volume":"246"},"journal_issn":null,"journal_title":null,"publication_types":[],"pubmed_pub_types":null,"s2_fields_of_study":["Mathematics"],"reference_count":24,"citation_count":24,"influential_citation_count":8,"is_open_access":false,"arxiv_categories":null,"arxiv_license":null,"arxiv_journal_ref":null,"mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":null,"s2_open_access_landing_url":null,"s2_open_access_license":null,"s2_open_access_status":null,"pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"Abstract We prove some global Morrey regularity results for almost minimizers of functionals of the form u ↦ ∫ Ω f ( x , ∇ u ) d x . This regularity is valid up to the boundary, provided the boundary data is sufficiently regular. The main assumption on f is that for each x, the function f ( x , ⋅ ) behaves asymptotically like a convex function with ( p , q ) growth. Some discontinuous behavior in the first argument is allowed. As a main application, we establish analogous regularity results for a broad class of systems of nonhomogeneous partial differential equations.","claims":[{"public_id":"cl_1a177ecc6da8f32cf0c5c94e0677ec92","status":"active","text":"Analogous regularity results are established for a broad class of nonhomogeneous partial differential equation systems.","confidence":0.96,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_1a177ecc6da8f32cf0c5c94e0677ec92"},{"public_id":"cl_4d22edcfd61ef55c531ddf28770afa78","status":"active","text":"Discontinuous dependence on the spatial variable in the integrand is allowed under the stated assumptions.","confidence":0.9,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous 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