dc.contributor.author Escauriaza, L. dc.contributor.author Montaner, S. dc.date.accessioned 2017-06-06T18:05:18Z dc.date.available 2017-06-06T18:05:18Z dc.date.issued 2017-05-30 dc.identifier.issn 1120-6330 dc.identifier.uri http://hdl.handle.net/20.500.11824/679 dc.description.abstract In this note we prove an end-point regularity result on the $L^P$ integrability of the second derivatives of solutions to non-divergence form uniformly elliptic equations whose second derivatives are a priori only known to be integrable. The main assumption on the elliptic operator is the Dini continuity of the coefficients. We provide a counterexample showing that the Dini condition is somehow optimal. We also give a counterexample related to the BMO regularity of second derivatives of solutions to elliptic equations. These results are analogous to corresponding results for divergence form elliptic equations in [3, 15]. en_US dc.format application/pdf en_US dc.language.iso eng en_US dc.rights Reconocimiento-NoComercial-CompartirIgual 3.0 España en_US dc.rights.uri http://creativecommons.org/licenses/by-nc-sa/3.0/es/ en_US dc.subject Regularity en_US dc.subject pathological solutions en_US dc.subject non-divergence form elliptic operator en_US dc.title Some remarks on the $L^p$ regularity of second derivatives of solutions to non-divergence elliptic equations and the Dini condition en_US dc.type info:eu-repo/semantics/article en_US dc.identifier.doi 10.4171/RLM/751 dc.relation.publisherversion http://www.ems-ph.org/journals/show_abstract.php?issn=1120-6330&vol=28&iss=1&rank=4 en_US dc.relation.projectID ES/1PE/SEV-2013-0323 en_US dc.relation.projectID ES/1PE/MTM2014-53145-P en_US dc.relation.projectID EUS/BERC/BERC.2014-2017 en_US dc.rights.accessRights info:eu-repo/semantics/openAccess en_US dc.type.hasVersion info:eu-repo/semantics/publishedVersion en_US dc.journal.title Rendiconti Lincei - Matematica e Applicazioni en_US
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