Optimal \(L^{p}\)- \(L^{q}\)-estimates for parabolic boundary value problems with inhomogeneous data

DOI10.1007/s00209-007-0120-9zbMath1210.35066OpenAlexW2052129269MaRDI QIDQ2384744

Robert Denk, Matthias Hieber, Jan W. Prüss

Publication date: 10 October 2007

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-007-0120-9

zbMATH Keywords

vector-valued Sobolev spacesparabolic boundary value problems with general boundary conditions

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Multipliers for harmonic analysis in several variables (42B15)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Imaginary powers of elliptic second order differential operators in \(L^ p\)-spaces
• Bounded \(H_ \infty\)-calculus for elliptic operators
• \(H_\infty \)-calculus for elliptic operators with non-smooth coefficients
• Functional calculi of second-order elliptic partial differential operators with bounded measurable coefficients
• Maximal \(L^p\)-regularity for elliptic operators with VMO-coefficients
• New thoughts on old results of R. T. Seeley
• Bounded holomorphic functional calculus for non-divergence form differential operators
• Functional calculi for linear operators in vector-valued \(L^p\)-spaces via the transference principle
• Semigroup kernels, Poisson bounds, and holomorphic functional calculus
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• $L^p-L^q$ ESTIMATES FOR PARABOLIC SYSTEMS IN NON-DIVERGENCE FORM WITH VMO COEFFICIENTS
• On operator-valued Fourier multiplier theorems
• On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems
• Heat kernels and maximal l^p—l^qestimates for parabolic evolution equations
• Analytic solutions for a Stefan problem with Gibbs-Thomson correction
• ℛ-boundedness, Fourier multipliers and problems of elliptic and parabolic type
• Maximal regularity for parabolic equations with inhomogeneous boundary conditions in Sobolev spaces with mixed $L_p$-norm
• ELLIPTIC PROBLEMS WITH A PARAMETER AND PARABOLIC PROBLEMS OF GENERAL TYPE
• A solution to the problem of \(L^p\)-maximal regularity
• Elliptic operators with infinite-dimensional state spaces
• Operator-valued Fourier multiplier theorems and maximal \(L_p\)-regularity
• The \(H^\infty\)-calculus and sums of closed operators
• Extrapolation of Carleson measures and the analyticity of Kato's square-root operators.