On divergence form second-order pdes with growing coefficients in W 1        p spaces without weights

N. V. Krylov

doi:10.1007/978-3-0348-0075-4_20

On divergence form second-order pdes with growing coefficients in W ¹ _p spaces without weights

N. V. Krylov

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

1 Scopus citations

Abstract

We consider second-order divergence form uniformly parabolic and elliptic PDEs with bounded and VMOx leading coefficients and possibly linearly growing lower-order coefficients. We look for solutions which are summable to the pth power with respect to the usual Lebesgue measure along with their first derivatives with respect to the spatial variables.

Original language	English (US)
Title of host publication	Progress in Nonlinear Differential Equations and Their Application
Publisher	Springer US
Pages	389-414
Number of pages	26
DOIs	https://doi.org/10.1007/978-3-0348-0075-4_20
State	Published - 2011

Publication series

Name	Progress in Nonlinear Differential Equations and Their Application
Volume	80
ISSN (Print)	1421-1750
ISSN (Electronic)	2374-0280

Bibliographical note

Publisher Copyright:
© 2011, Springer Basel AG.

Keywords

Divergence type equations
Growing coefficients
Sobolev spaces without weights
Stochastic partial differential equations

Publisher link

10.1007/978-3-0348-0075-4_20

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abstract = "We consider second-order divergence form uniformly parabolic and elliptic PDEs with bounded and VMOx leading coefficients and possibly linearly growing lower-order coefficients. We look for solutions which are summable to the pth power with respect to the usual Lebesgue measure along with their first derivatives with respect to the spatial variables.",

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KW - Growing coefficients

KW - Sobolev spaces without weights

KW - Stochastic partial differential equations

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