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L2-solvability of the Dirichlet, Neumann and 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. Nazarbayev Univ, Dept Math, Astana 010000, Kazakhstan..
Stockholm Univ, Dept Math, SE-10691 Stockholm, Sweden..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
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
Identifiers
URN: urn:nbn:se:uu:diva-340893DOI: 10.1090/tran/6958ISI: 000414149300010OAI: oai:DiVA.org:uu-340893DiVA, id: diva2:1181005
Funder
Swedish Research Council, 621-2011-3629The Crafoord FoundationAvailable from: 2018-02-07 Created: 2018-02-07 Last updated: 2018-02-07Bibliographically approved

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Castro, Alejandro J.Staubach, Wolfgang

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