The boundary regularity of non-linear parabolic systems I

DOI10.1016/j.anihpc.2009.09.003zbMath1194.35086OpenAlexW4206521926WikidataQ58880847 ScholiaQ58880847MaRDI QIDQ846394

Frank Duzaar, Verena Bögelein, Giuseppe Mingione

Publication date: 9 February 2010

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.anihpc.2009.09.003

zbMATH Keywords

Cauchy-Dirichlet problemMorrey space\(A\)-caloric approximation lemmaregular boundary point

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Degenerate parabolic equations (35K65) Quasilinear parabolic equations (35K59) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items (35)

Regularity of solutions of the model Venttsel' problem for quasilinear parabolic systems with nonsmooth in time principal matrices ⋮ Partial regularity for subquadratic parabolic systems under controllable growth conditions ⋮ The boundary regularity of non-linear parabolic systems. II ⋮ Partial regularity for solutions of quasilinear parabolic systems with nonsmooth in time principal matrix ⋮ Fractional differentiability for solutions of a class of parabolic systems with \(L^{1,\theta}\)-data ⋮ Regularity of weak solutions to a class of nonlinear problem ⋮ Global Calderón-Zygmund estimate for \(p\)-Laplacian parabolic system ⋮ Regularity of solutions to quasilinear parabolic systems with time-nonsmooth principal matrix and the Neumann boundary condition ⋮ Regularity of weak solutions to linear and quasilinear parabolic systems of non-divergence type with non-smooth in time principal matrix: \(A(t)\)-caloric method ⋮ Morrey estimates for solutions of singular quadratic nonlinear equations ⋮ Global gradient bounds for the parabolicp-Laplacian system ⋮ \(\mathcal{A}\)-caloric approximation and partial regularity for parabolic systems with Orlicz growth ⋮ Regularity results for solutions of a class of parabolic systems with measure data ⋮ Regularity in parabolic systems with continuous coefficients ⋮ Partial regularity for parabolic systems with non-standard growth ⋮ Construction of solutions to parabolic and hyperbolic initial–boundary value problems ⋮ Partial regularity for subquadratic parabolic systems by \(\mathcal{A}\)-caloric approximation ⋮ Partial regularity for subquadratic parabolic systems with continuous coefficients ⋮ Calderón-Zygmund estimates for parabolic measure data equations ⋮ Global weighted estimates for the gradient of solutions to nonlinear elliptic equations ⋮ Regularity problem for \(2m\)-order quasilinear parabolic systems with non smooth in time principal matrix. \((A(t),m)\)-caloric approximation method ⋮ A non-local problem for the Fokker-Planck equation related to the Becker-Döring model ⋮ Parabolic equations and the bounded slope condition ⋮ Boundary regularity in variational problems ⋮ Regularity of weak solutions to the model Venttsel problem for linear parabolic systems with nonsmooth in time principal matrix: \(A(t)\)-caloric approximation method ⋮ Regularity of solutions to a model oblique derivative problem for quasilinear parabolic systems with nondiagonal principal matrices ⋮ Regularity problem for one class of nonlinear parabolic systems with non-smooth in time principal matrices ⋮ Partial regularity for doubly nonlinear parabolic systems of the first type ⋮ The one-sided bounded slope condition in evolution problems ⋮ The regularity of general parabolic systems with degenerate diffusion ⋮ Global Regularity of Weak Solutions to Quasilinear Elliptic and Parabolic Equations with Controlled Growth ⋮ Parabolic Systems with Polynomial Growth and Regularity ⋮ Boundary partial regularity for minimizers of discontinuous quasiconvex integrals with general growth ⋮ Boundary partial regularity for solutions of quasilinear parabolic systems with non smooth in time principal matrix ⋮ Hölder estimates for parabolic obstacle problems

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