\(L^2\) well-posedness of boundary value problems for parabolic systems with measurable coefficients

DOI10.4171/JEMS/980zbMath1454.35209arXiv1607.06246OpenAlexW3035426744MaRDI QIDQ2216730

Pascal Auscher, Moritz Egert, Kaj Nyström

Publication date: 17 December 2020

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.06246

zbMATH Keywords

Dirichlet and Neumann problemssquare function estimateshalf-order derivativeparabolic Dirac operatorparabolic Kato square root estimate(non-tangential) maximal functionsboundary layer operators

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) One-parameter semigroups and linear evolution equations (47D06) Fractional derivatives and integrals (26A33) Functional calculus for linear operators (47A60) PDEs with low regular coefficients and/or low regular data (35R05) Harmonic analysis and PDEs (42B37) Initial-boundary value problems for second-order parabolic systems (35K51)

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A universal variational framework for parabolic equations and systems ⋮ On Kato square root problem for a parabolic operator and applications ⋮ A note on a modified Hilbert transform ⋮ Tent space well-posedness for parabolic Cauchy problems with rough coefficients ⋮ On the fine properties of parabolic measures associated to strongly degenerate parabolic operators of Kolmogorov type ⋮ The square root of a parabolic operator ⋮ Hardy spaces for boundary value problems of elliptic systems with block structure ⋮ The Dirichlet-conormal problem for the heat equation with inhomogeneous boundary conditions ⋮ On local regularity estimates for fractional powers of parabolic operators with time-dependent measurable coefficients ⋮ Commutator estimates for the Dirichlet-to-Neumann map associated to parabolic equations with complex-valued and measurable coefficients on \(\mathbb{R}_+^{n + 2} \)

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