Fully nonlinear elliptic and parabolic equations in weighted and mixed-norm Sobolev spaces

Hongjie Dong; N. V. Krylov

doi:10.1007/s00526-019-1591-3

Fully nonlinear elliptic and parabolic equations in weighted and mixed-norm Sobolev spaces

Hongjie Dong
, N. V. Krylov

School of Mathematics

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

We present the first to date weighted and mixed-norm Sobolev estimates for fully nonlinear elliptic and parabolic equations in the whole space under a relaxed convexity condition with almost VMO dependence on space-time variables. The corresponding interior and boundary estimates are also obtained.

Original language	English (US)
Article number	145
Journal	Calculus of Variations and Partial Differential Equations
Volume	58
Issue number	4
DOIs	https://doi.org/10.1007/s00526-019-1591-3
State	Published - Aug 1 2019

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© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.

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10.1007/s00526-019-1591-3

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title = "Fully nonlinear elliptic and parabolic equations in weighted and mixed-norm Sobolev spaces",

abstract = "We present the first to date weighted and mixed-norm Sobolev estimates for fully nonlinear elliptic and parabolic equations in the whole space under a relaxed convexity condition with almost VMO dependence on space-time variables. The corresponding interior and boundary estimates are also obtained.",

author = "Hongjie Dong and Krylov, \{N. V.\}",

note = "Publisher Copyright: {\textcopyright} 2019, Springer-Verlag GmbH Germany, part of Springer Nature.",

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AU - Dong, Hongjie

AU - Krylov, N. V.

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N2 - We present the first to date weighted and mixed-norm Sobolev estimates for fully nonlinear elliptic and parabolic equations in the whole space under a relaxed convexity condition with almost VMO dependence on space-time variables. The corresponding interior and boundary estimates are also obtained.

AB - We present the first to date weighted and mixed-norm Sobolev estimates for fully nonlinear elliptic and parabolic equations in the whole space under a relaxed convexity condition with almost VMO dependence on space-time variables. The corresponding interior and boundary estimates are also obtained.

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M3 - Article

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Fully nonlinear elliptic and parabolic equations in weighted and mixed-norm Sobolev spaces

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