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  • Castro, Alejandro, J.Uppsala universitet,Analys och sannolikhetsteori (author)

L2 Solvability of the Dirichlet, Neumann and the regularity problems for parabolic equations with time-independent Hölder-continuous coefficients

  • Article/chapterEnglish2024

Publisher, publication year, extent ...

  • American Mathematical Society (AMS),2024
  • printrdacarrier

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  • LIBRIS-ID:oai:DiVA.org:uu-284860
  • https://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-284860URI

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  • Language:English
  • Summary in:English

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  • Subject category:ref swepub-contenttype
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  • 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.

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  • Rodríguez-López, Salvador (author)
  • Staubach, Wolfgang (author)
  • Uppsala universitetAnalys och sannolikhetsteori (creator_code:org_t)

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  • In:Transactions of the American Mathematical Society: American Mathematical Society (AMS)0002-99471088-6850

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