Existence and global second-order regularity for anisotropic parabolic equations with variable growth

Arora, Rakesh

dc.contributor.author	Arora, Rakesh
dc.date.accessioned	2024-03-13T09:21:03Z
dc.date.available	2024-03-13T09:21:03Z
dc.date.issued	2022-12-21
dc.identifier.issn	00220396
dc.identifier.uri	http://localhost:8080/xmlui/handle/123456789/2983
dc.description	This paper published with affiliation IIT (BHU), Varanasi in open access mode.	en_US
dc.description.abstract	We consider the homogeneous Dirichlet problem for the anisotropic parabolic equation ut−∑i=1NDx(\|Dxu\|pDxu)=f(x,t) in the cylinder Ω×(0,T), where Ω⊂RN, N≥2, is a parallelepiped. The exponents of nonlinearity pi are given Lipschitz-continuous functions. It is shown that if [Formula presented], [Formula presented] then the problem has a unique solution u∈C([0,T];L2(Ω)) with \|Dxu\|p∈L∞(0,T;L1(Ω)), ut∈L2(QT). Moreover, [Formula presented] The assertions remain true for a smooth domain Ω if pi=2 on the lateral boundary of QT.	en_US
dc.language.iso	en	en_US
dc.publisher	Academic Press Inc.	en_US
dc.relation.ispartofseries	Journal of Differential Equations;349
dc.subject	Anisotropic nonlinearity	en_US
dc.subject	Global higher integrability	en_US
dc.subject	Nonlinear parabolic equations	en_US
dc.subject	Second-order regularity	en_US
dc.title	Existence and global second-order regularity for anisotropic parabolic equations with variable growth	en_US
dc.type	Article	en_US