Sobolev Space Theory of Parabolic Equations Degenerating on the Boundary ofC1Domains

DOI10.1080/03605300600910449zbMath1124.35031OpenAlexW2087480171MaRDI QIDQ5421520

Kyeong-Hun Kim

Publication date: 24 October 2007

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605300600910449

zbMATH Keywords

existence and uniquenessHölder estimatesSobolev spaces with weights

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) Degenerate parabolic equations (35K65) A priori estimates in context of PDEs (35B45)

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Multi-dimensional degenerate operators in \(L^p\)-spaces ⋮ Linear parabolic equations with strong boundary degeneration ⋮ Nondivergence form degenerate linear parabolic equations on the upper half space ⋮ Degenerate operators of Tricomi type in \(L^p\)-spaces and in spaces of continuous functions ⋮ Second order elliptic operators in \(L^2\) with first order degeneration at the boundary and outward pointing drift ⋮ On the second order derivative estimates for degenerate parabolic equations ⋮ A weighted Sobolev regularity theory of the parabolic equations with measurable coefficients on conic domains in \(\mathbb{R}^d\) ⋮ On the heat diffusion starting with degeneracy ⋮ A \(W_p^n\)-theory of parabolic equations with unbounded leading coefficients on non-smooth domains

Cites Work

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• On The Sobolev Space Theory of Parabolic and Elliptic Equations inC¹Domains
• A Sobolev Space Theory of SPDEs with Constant Coefficients in a Half Space
• BOUNDARY VALUE PROBLEMS FOR ELLIPTIC EQUATIONS DEGENERATE ON THE BOUNDARY OF A DOMAIN
• Sobolev spaces with weights in domains and boundary value problems for degenerate elliptic equations

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