The Laplacian on cylindrical domains

DOI10.1007/s00020-012-2031-3zbMath1268.35039OpenAlexW2169110932MaRDI QIDQ1946562

Tobias Nau

Publication date: 15 April 2013

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00020-012-2031-3

zbMATH Keywords

periodic boundary conditionsLaplacianelliptic regularityoperator-valued Fourier multiplierscylindrical domainsmaximal parabolic regularitymixed Dirichlet-Neumann boundary conditions\({\mathcal{R}}\)-boundedness

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Heat equation (35K05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Applications of functional analysis to differential and integral equations (46N20)

Related Items (6)

\(L^p-L^q\)-maximal regularity of the Van Wijngaarden-Eringen equation in a cylindrical domain ⋮ Global strong solutions for a class of heterogeneous catalysis models ⋮ Strongly \(L^p\) well-posedness for abstract time-fractional Moore-Gibson-Thompson type equations ⋮ Periodic solutions for the Blackstock-Crighton-Westervelt equation ⋮ A characterization of \(L^p\)-maximal regularity for time-fractional systems in \textit{UMD} spaces and applications ⋮ Local strong solutions for the non-linear thermoelastic plate equation on rectangular domains in \(L^p\)-spaces

Cites Work

• The operator-valued Marcinkiewicz multiplier theorem and maximal regularity
• On operator-valued Fourier multipliers
• Maximal \(L^{p}\)-regularity for the Laplacian on Lipschitz domains
• Operator-valued Fourier multiplier theorems on \(L_p\)-spaces on \(\mathbb{T}^d\)
• The inhomogeneous Dirichlet problem in Lipschitz domains
• \(H^\infty\)-calculus for cylindrical boundary value problems
• The functional calculus for sectorial operators
• Lp-Theory of Cylindrical Boundary Value Problems
• R-sectoriality of Cylindrical Boundary Value Problems
• On operator-valued Fourier multiplier theorems
• Pseudo-Differential Operators and Symmetries
• Discrete Fourier multipliers and cylindrical boundary-value problems
• Operator-valued Fourier multiplier theorems and maximal \(L_p\)-regularity
• The \(H^\infty\)-calculus and sums of closed operators
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