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L2 Solvability of the Dirichlet, Neumann and the regularity problems for parabolic equations with time-independent Hölder-continuous coefficients
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
(English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850Article in journal (Refereed) Accepted
Abstract [en]

We establish the $L^2$-solvability of Dirichlet, Neumann and regularity problems for divergence-form heat (or diffusion) equations with time-independent H\"older-continuous diffusion coefficients, on bounded Lipschitz domains in $\mathbb{R}^n$. This is achieved through the demonstration of invertibility of the relevant layer-potentials which is in turn based on Fredholm theory and a systematic transference scheme which yields suitable parabolic Rellich-type estimates.

Place, publisher, year, edition, pages
American Mathematical Society (AMS).
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Mathematical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-284860OAI: oai:DiVA.org:uu-284860DiVA: diva2:920928
Available from: 2016-04-19 Created: 2016-04-19 Last updated: 2017-11-30

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