Morrey estimates and Hölder continuity for solutions to parabolic equations with entropy inequalities

DOI10.1515/CRELLE.2010.006zbMath1191.35077OpenAlexW1996782603MaRDI QIDQ3404383

Jens Frehse, Maria Specovius-Neugebauer

Publication date: 9 February 2010

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/crelle.2010.006

zbMATH Keywords

weighted estimatestwo space dimensionsnonlinear parabolic systemsmeasure valued solutionshole filling techniquecontinuous linear spline functions

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear parabolic equations (35K55) A priori estimates in context of PDEs (35B45) Initial value problems for second-order parabolic systems (35K45)

Related Items (5)

On regularity of weak solutions to linear parabolic systems with measurable coefficients ⋮ Existence of regular solutions to a class of parabolic systems in two space dimensions with critical growth behaviour ⋮ Global solvability of the Cauchy-Dirichlet problem for a class of strongly nonlinear parabolic systems ⋮ Weak global solvability of the two-phase problem for a class of parabolic systems with strong nonlinearity in the gradient. The case of two spatial variables ⋮ Heat flow for a class of quadratic functionals with nondiagonal principal matrix. Existence of a smooth global solution

Cites Work

• On two-dimensional quasi-linear elliptic systems
• On the nonlinear parabolic systems in divergence form. Hölder continuity and partial Hölder continuity of the solutions
• On the Hölder continuity of bounded weak solutions of quasilinear parabolic systems
• On the Hölder continuity of bounded weak solutions of quasi-linear parabolic inequalities
• Full regularity for a class of degenerated parabolic systems in two spatial variables
• Hölder continuity of solutions of elliptic systems
• Continuity of Solutions of Parabolic and Elliptic Equations
• Regularity of Solutions for Some Quasilinear Parabolic Systems
• Smooth Solutions of systems of quasilinear parabolic equations
• InteriorC^{1, γ}-Regularity for Weak Solutions of Nonlinear Second Order Parabolic Systems
• A harnack inequality for parabolic differential equations

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