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L2-solvability of the Dirichlet, Neumann and regularity problems for parabolic equations with time-independent Hölder-continuous coefficients
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0002-7882-4013
2018 (English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 370, no 1, p. 265-319Article in journal (Refereed) Published
Abstract [en]

We establish the L-2-solvability of Dirichlet, Neumann and regularity problems for divergence-form heat (or diffusion) equations with timeindependent Holder-continuous diffusion coefficients on bounded Lipschitz domains in 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
2018. Vol. 370, no 1, p. 265-319
Keywords [en]
Boundary value problems, parabolic equations, Lipschitz domains, layer potentials, Rellich estimates
National Category
Mathematics
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-149934DOI: 10.1090/tran/6958ISI: 000414149300010OAI: oai:DiVA.org:su-149934DiVA, id: diva2:1164725
Projects
MTM2013-40985-PAvailable from: 2017-12-11 Created: 2017-12-11 Last updated: 2017-12-12Bibliographically approved

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