Equivalence of weak and viscosity solutions for the nonhomogeneous double phase equation

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dc.contributor.authorFang, Yuzhoucs
dc.contributor.authorRadulescu, Vicentiucs
dc.contributor.authorZhang, Chaocs
dc.coverage.issue3cs
dc.coverage.volume388cs
dc.date.issued2024-01-15cs
dc.description.abstractWe establish the equivalence between weak and viscosity solutions to the nonhomogeneous double phase equation with lower-order term - div(|Du|(p-2)Du+a(x)|Du|(q-2)Du)= f (x, u, Du), 1 < p <= q < infinity, a(x) >= 0. We find some appropriate hypotheses on the coefficient a(x), the exponents p, q and the nonlinear term f to show that the viscosity solutions with a priori Lipschitz continuity are weak solutions of such equation by virtue of the inf(sup)-convolution techniques. The reverse implication can be concluded through comparison principles. Moreover, we verify that the bounded viscosity solutions are exactly Lipschitz continuous, which is also of independent interest.en
dc.formattextcs
dc.format.extent2519-2559cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationMATHEMATISCHE ANNALEN. 2024, vol. 388, issue 3, p. 2519-2559.en
dc.identifier.doi10.1007/s00208-023-02593-ycs
dc.identifier.issn0025-5831cs
dc.identifier.orcid0000-0003-4615-5537cs
dc.identifier.other183167cs
dc.identifier.researcheridA-1503-2012cs
dc.identifier.scopus35608668800cs
dc.identifier.urihttp://hdl.handle.net/11012/244281
dc.language.isoencs
dc.publisherSpringer Naturecs
dc.relation.ispartofMATHEMATISCHE ANNALENcs
dc.relation.urihttps://www.webofscience.com/wos/woscc/full-record/WOS:000940224800001cs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/0025-5831/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectregularityen
dc.subjectfunctionalsen
dc.titleEquivalence of weak and viscosity solutions for the nonhomogeneous double phase equationen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-183167en
sync.item.dbtypeVAVen
sync.item.insts2025.02.03 15:40:50en
sync.item.modts2025.01.17 15:21:18en
thesis.grantorVysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií. Ústav matematikycs
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