On the sobolev space theory of parabolic and elliptic equations in C 1 domains

Kyeong Hun Kim; N. V. Krylov

doi:10.1137/S0036141003421145

On the sobolev space theory of parabolic and elliptic equations in C ¹ domains

Kyeong Hun Kim, N. V. Krylov

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

49 Citations (Scopus)

Abstract

Existence and uniqueness results are given for second-order parabolic and elliptic equations with variable coefficients in C ¹ domains in Sobolev spaces with weights allowing the derivatives of solutions to blow up near the boundary. The "number" of derivatives can be negative and fractional. The coefficients of parabolic equations are only assumed to be measurable in time.

Original language	English
Pages (from-to)	618-642
Number of pages	25
Journal	SIAM Journal on Mathematical Analysis
Volume	36
Issue number	2
DOIs	https://doi.org/10.1137/S0036141003421145
Publication status	Published - 2005
Externally published	Yes

Keywords

C domains
Parabolic equations
Sobolev spaces with weights

ASJC Scopus subject areas

Analysis
Computational Mathematics
Applied Mathematics

Access to Document

10.1137/S0036141003421145

Cite this

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KW - Sobolev spaces with weights

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