L2-solvability of the dirichlet, neumann and regularity problems for parabolic equations with time-independent hölder-continuous coefficients

Alejandro J. Castro; Salvador Rodríguez-López; Wolfgang Staubach

doi:10.1090/tran/6958

L²-solvability of the dirichlet, neumann and regularity problems for parabolic equations with time-independent hölder-continuous coefficients

Alejandro J. Castro, Salvador Rodríguez-López, Wolfgang Staubach

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

We establish the L² -solvability of Dirichlet, Neumann and regularity problems for divergence-form heat (or diffusion) equations with time-independent Hölder-continuous diffusion coefficients on bounded Lipschitz domains in ℝⁿ. 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.

Original language	English
Pages (from-to)	265-319
Number of pages	55
Journal	Transactions of the American Mathematical Society
Volume	370
Issue number	1
DOIs	https://doi.org/10.1090/tran/6958
Publication status	Published - Jan 1 2018

Keywords

Boundary value problems
Layer potentials
Lipschitz domains
Parabolic equations
Rellich estimates

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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L²-solvability of the dirichlet, neumann and regularity problems for parabolic equations with time-independent hölder-continuous coefficients. / Castro, Alejandro J.; Rodríguez-López, Salvador; Staubach, Wolfgang.

In: Transactions of the American Mathematical Society, Vol. 370, No. 1, 01.01.2018, p. 265-319.

Research output: Contribution to journal › Article › peer-review

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abstract = "We establish the L2 -solvability of Dirichlet, Neumann and regularity problems for divergence-form heat (or diffusion) equations with time-independent H{\"o}lder-continuous diffusion coefficients on bounded Lipschitz domains in ℝn. 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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