Parabolic equations with \(p,q\)-growth

DOI10.1016/j.matpur.2013.01.012zbMath1288.35302OpenAlexW111793035MaRDI QIDQ391499

Frank Duzaar, Paolo Marcellini, Verena Bögelein

Publication date: 10 January 2014

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2013.01.012

zbMATH Keywords

Cauchy-Dirichlet problemgradient estimatesnonstandard \(p,q\)-growth

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Weak solutions to PDEs (35D30) Quasilinear parabolic equations (35K59)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Higher differentiability of minimizers of convex variational integrals
• Degenerate parabolic equations
• Regularity for elliptic equations with general growth conditions
• Nonlinear elliptic systems with general growth
• Regularity of relaxed minimizers of quasiconvex variational integrals with \((p, q)\)-growth
• Boundedness of the gradient for a doubly nonlinear parabolic equation
• Regularity under sharp anisotropic general growth conditions
• Existence and uniqueness of weak solutions for a non-uniformly parabolic equation
• Compact sets in the space \(L^ p(0,T;B)\)
• Regularity of minimizers of integrals of the calculus of variations with non-standard growth conditions
• Regularity results for parabolic systems related to a class of non-Newtonian fluids.
• Higher integrability for minimizers of integral functionals with \((p,q)\) growth
• Gradient estimates for anisotropic elliptic equations
• Regularity and existence of solutions of elliptic equations with p,q- growth conditions
• Parabolic Systems with Polynomial Growth and Regularity
• Hölder estimates for nonlinear degenerate parabolic sytems.
• Regularity theorems for degenerate quasiconvex energies with (p, q)-growth
• Regularity of solutions of certain parabolic system with nonstandard growth condition
• The regularity of general parabolic systems with degenerate diffusion

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