Solutions for quasilinear nonsmooth evolution systems in \(L^p\)

DOI10.1007/s00205-003-0297-yzbMath1053.35058OpenAlexW2158999556MaRDI QIDQ1879431

Joachim Rehberg, Gunther Schmidt, Vladimir Gilelevich Maz'ya, Johannes Elschner

Publication date: 22 September 2004

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00205-003-0297-y

zbMATH Keywords

Dirichlet problemGreen's functionpointwise estimatelocal solvabilitypiecewise constant coefficientsisotropic materialsinterface problemsthree-dimensional polyhedral space domain

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Reaction-diffusion equations (35K57)

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Cites Work

• On the Hölder continuity of bounded weak solutions of quasilinear parabolic systems
• Local existence for quasilinear parabolic systems under nonlinear boundary conditions
• Global solutions to a class of strongly coupled parabolic systems
• The inhomogeneous Dirichlet problem in Lipschitz domains
• Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus
• On the poisson equation with intersecting interfaces
• The Thermistor Problem: Existence, Smoothness Uniqueness, Blowup
• Interpolation for Function Spaces Related to Mixed Boundary Value Problems
• Fast semi-analytic computation of elastic edge singularities
• Regularity results for Laplace interface problems in two dimensions
• Russian Language Ignored
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