Coercivity for elliptic operators and positivity of solutions on Lipschitz domains

DOI10.1007/s00013-010-0184-3zbMath1205.35065OpenAlexW1992361579MaRDI QIDQ607710

Robert Haller-Dintelmann, Joachim Rehberg

Publication date: 3 December 2010

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00013-010-0184-3

zbMATH Keywords

coercivitypositivity of solutionsmixed boundary problems

Mathematics Subject Classification ID

Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) PDEs with low regular coefficients and/or low regular data (35R05) Weak solutions to PDEs (35D30) Variational methods for second-order elliptic equations (35J20) Positive solutions to PDEs (35B09)

Related Items (11)

Maximal Parabolic Regularity for Divergence Operators on Distribution Spaces ⋮ Hölder-estimates for non-autonomous parabolic problems with rough data ⋮ Quasilinear elliptic and parabolic Robin problems on Lipschitz domains ⋮ Optimal Control of the Thermistor Problem in Three Spatial Dimensions, Part 2: Optimality Conditions ⋮ Optimal Control of the Thermistor Problem in Three Spatial Dimensions, Part 1: Existence of Optimal Solutions ⋮ Optimal control of a parabolic equation with dynamic boundary condition ⋮ Parabolic equations with dynamical boundary conditions and source terms on interfaces ⋮ On maximal parabolic regularity for non-autonomous parabolic operators ⋮ Unnamed Item ⋮ The 3D transient semiconductor equations with gradient-dependent and interfacial recombination ⋮ The square root problem for second-order, divergence form operators with mixed boundary conditions on \(L^p\)

Cites Work

• Maximal parabolic regularity for divergence operators including mixed boundary conditions
• The embedding of the positive cone of $H^{-1}$ in $W^{-1,\,q}$ is compact for all $q<2$ (with a remark of Haim Brezis)
• About a stationary Schrödinger-Poisson system with Kohn-Sham potential in a bounded two- or three-dimensional domain
• Weakly Differentiable Functions
• Sets of Finite Perimeter and the Gauss-Green Theorem with Singularities
• Gauss‐Green theorem for weakly differentiable vector fields, sets of finite perimeter, and balance laws
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