@article{7cd42809e5e64d15a9375659fda4dcd6,
title = "L2-solvability of the dirichlet, neumann and regularity problems for parabolic equations with time-independent h{\"o}lder-continuous coefficients",
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.",
keywords = "Boundary value problems, Layer potentials, Lipschitz domains, Parabolic equations, Rellich estimates",
author = "Castro, {Alejandro J.} and Salvador Rodr{\'i}guez-L{\'o}pez and Wolfgang Staubach",
note = "Funding Information: Received by the editors March 18, 2016. 2010 Mathematics Subject Classification. Primary 35K20, 42B20. Key words and phrases. Boundary value problems, parabolic equations, Lipschitz domains, layer potentials, Rellich estimates. The first author was partially supported by Swedish Research Council Grant 621-2011-3629. The second author was partially supported by Spanish Government grant MTM2013-40985-P. The third author was partially supported by a grant from the Crafoord Foundation. Publisher Copyright: {\textcopyright} 2017 American Mathematical Society. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.",
year = "2018",
month = jan,
day = "1",
doi = "10.1090/tran/6958",
language = "English",
volume = "370",
pages = "265--319",
journal = "Transactions of the American Mathematical Society",
issn = "0002-9947",
publisher = "American Mathematical Society",
number = "1",
}