L∞-ESTIMATES FOR DIVERGENCE OPERATORS ON BAD DOMAINS

DOI10.1142/S0219530512500091zbMath1242.35069OpenAlexW1972515443MaRDI QIDQ2883132

Joachim Rehberg, A. F. M. ter Elst

Publication date: 11 May 2012

Published in: Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219530512500091

zbMATH Keywords

mixed Dirichlet-Neumann conditionsDirichlet boundary part

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for second-order elliptic equations (35J25) Functional calculus for linear operators (47A60) A priori estimates in context of PDEs (35B45) PDEs with low regular coefficients and/or low regular data (35R05)

Related Items (12)

Elliptic and parabolic regularity for second- order divergence operators with mixed boundary conditions ⋮ Transmission problems with nonlocal boundary conditions and rough dynamic interfaces ⋮ On \(p\)-elliptic divergence form operators and holomorphic semigroups ⋮ Second order optimality conditions for optimal control of quasilinear parabolic equations ⋮ Optimal control of reaction-diffusion systems with hysteresis ⋮ Parabolic equations with dynamical boundary conditions and source terms on interfaces ⋮ Stability of square root domains associated with elliptic systems of PDEs on nonsmooth domains ⋮ On maximal parabolic regularity for non-autonomous parabolic operators ⋮ The 3D transient semiconductor equations with gradient-dependent and interfacial recombination ⋮ On the \(\mathrm{L}^p\)-theory for second-order elliptic operators in divergence form with complex coefficients ⋮ The square root problem for second-order, divergence form operators with mixed boundary conditions on \(L^p\) ⋮ Hardy's inequality for functions vanishing on a part of the boundary

Cites Work

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• Maximal parabolic regularity for divergence operators including mixed boundary conditions
• Hölder continuity and optimal control for nonsmooth elliptic problems
• Semigroups of linear operators and applications to partial differential equations
• A \(W^{1,p}\)-estimate for solutions to mixed boundary value problems for second order elliptic differential equations
• Every superposition operator mapping one Sobolev space into another is continuous
• Linear and quasilinear elliptic equations
• Linear Elliptic Boundary Value Problems with Non-Smooth Data: Campanato Spaces of Functionals
• Elliptic Partial Differential Equations of Second Order

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