Local existence, uniqueness and smooth dependence for nonsmooth quasilinear parabolic problems

DOI10.1007/s00028-010-0052-4zbMath1239.35084OpenAlexW1985959990MaRDI QIDQ423411

Lutz Recke, Jens André Griepentrog

Publication date: 2 June 2012

Published in: Journal of Evolution Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00028-010-0052-4

zbMATH Keywords

mixed boundary conditionsimplicit function theoremmaximal regularitysets with Lipschitz boundarySobolev-Morrey spaces

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear parabolic equations (35K55) Abstract parabolic equations (35K90) Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60) PDEs with low regular coefficients and/or low regular data (35R05) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Related Items

Hopf bifurcation for general 1D semilinear wave equations with delay, Existence theory for rosseland equation and its homogenized equation, Quasilinear elliptic and parabolic Robin problems on Lipschitz domains, Interior Hölder and gradient estimates for the homogenization of the linear elliptic equations, Uniqueness of strong solutions and weak-strong stability in a system of cross-diffusion equations, Cross-diffusion systems with non-zero flux and moving boundary conditions, Solution regularity and smooth dependence for abstract equations and applications to hyperbolic PDEs, Global Regularity and Multiscale Approach for Thermal Radiation Heat Transfer, Quasi-Linear Parabolic Reaction-Diffusion Systems: A User's Guide to Well-Posedness, Spectra, and Stability of Travelling Waves

Cites Work

• Maximal parabolic regularity for divergence operators including mixed boundary conditions
• Applications of differential calculus to quasilinear elliptic boundary value problems with non-smooth data
• Sobolev-Morrey spaces associated with evolution equations
• Maximal regularity for nonsmooth parabolic problems in Sobolev-Morrey spaces
• Regularity and nonuniqueness results for parabolic problems arising in some physical models, having natural growth in the gradient
• A \(W^{1,p}\)-estimate for solutions to mixed boundary value problems for second order elliptic differential equations
• On the uniqueness of solutions for nonlinear elliptic-parabolic equations
• On unique solvability of nonlocal drift--diffusion-type problems.
• Linear and quasilinear parabolic equations in Sobolev space
• Solutions for quasilinear nonsmooth evolution systems in \(L^p\)
• Quasilinear parabolic problems via maximal regularity
• Analyticity of solutions to nonlinear parabolic equations on manifolds and an application to Stokes flow
• Equazioni paraboliche del secondo ordine e spazi \({\mathfrak L}^{2,\theta} (\Omega,\delta)\)
• Spazi \({\mathcal L}^{(p,\vartheta)} (\Omega,\delta)\) e loro proprieta
• Linear Elliptic Boundary Value Problems with Non-Smooth Data: Campanato Spaces of Functionals
• Existence and Uniqueness Results for Reaction-diffusion Processes of Electrically Charged Species
• Quasilinear Parabolic Systems with Mixed Boundary Conditions on Nonsmooth Domains
• Non-local quasi-linear parabolic equations
• Maximal regularity in continuous interpolation spaces and quasilinear parabolic equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item