On the property of higher integrability for parabolic systems of variable order of nonlinearity

DOI10.1134/S0001434610010256zbMath1204.35060OpenAlexW1978524918MaRDI QIDQ1957034

S. E. Pastukhova, Vasilii V. Jikov

Publication date: 24 September 2010

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0001434610010256

zbMATH Keywords

Gehring's lemmaSobolev-Poincaré inequalitiesSobolev-Orlicz spacehigher integrability of the gradientCacciopolli's inequalityHölder's reverse inequalitypower growth conditions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) A priori estimates in context of PDEs (35B45) Second-order parabolic systems (35K40) Quasilinear parabolic equations (35K59)

Related Items (24)

Harnack's inequality for singular parabolic equations with generalized Orlicz growth under the non-logarithmic Zhikov's condition ⋮ On the continuity of solutions of quasilinear parabolic equations with generalized Orlicz growth under non-logarithmic conditions ⋮ Global higher regularity of solutions to singular \(p(x,t)\)-parabolic equations ⋮ Global a priori bounds for weak solutions to quasilinear parabolic equations with nonstandard growth ⋮ Parabolic systems with \({p,q}\)-growth: a variational approach ⋮ Existence and regularity results for a class of parabolic problems with double phase flux of variable growth ⋮ Hölder estimates for parabolic \(p(x, t)\)-Laplacian systems ⋮ Higher integrability for solutions to parabolic problems with irregular obstacles and nonstandard growth ⋮ Existence theorems for solutions of parabolic equations with variable order of nonlinearity ⋮ Lemmas on compensated compactness in elliptic and parabolic equations ⋮ Local higher integrability for unsteady motion equations of generalized Newtonian fluids ⋮ \( {\mathfrak{B}}_1\) classes of De Giorgi, Ladyzhenskaya, and Ural'tseva and their application to elliptic and parabolic equations with nonstandard growth ⋮ Partial regularity for parabolic systems with non-standard growth ⋮ Estimates of decay rate for solution to parabolic equation with non-power nonlinearities ⋮ Strong solutions of evolution equations with \(p(x,t)\)-Laplacian: existence, global higher integrability of the gradients and second-order regularity ⋮ Very weak solutions of degenerate parabolic systems with non-standard \(p(x,t)\)-growth ⋮ Higher regularity of solutions of singular parabolic equations with variable nonlinearity ⋮ The one dimensional parabolic \(p(x)\)-Laplace equation ⋮ Compact embedding for \(p(x,t)\)-Sobolev spaces and existence theory to parabolic equations with \(p(x,t)\)-growth ⋮ Compensated compactness principle and solvability of generalized Navier-Stokes equations ⋮ Lipschitz regularity for viscosity solutions to parabolic \({p(x,t)}\)-Laplacian equations on Riemannian manifolds ⋮ Elliptic problems with nonstandard conditions of growth: Zhikov's approach ⋮ Global estimates for solutions of singular parabolic and elliptic equations with variable nonlinearity ⋮ Global higher integrability for symmetric \(p(x, t)\)-Laplacian system

Cites Work

• Unnamed Item
• Degenerate parabolic equations
• Higher integrability for parabolic systems of \(p\)-Laplacian type
• Higher integrability for parabolic equations of \(p(x,t)\)-Laplacian type
• The L\(^p\)-integrability of the partial derivatives of a quasiconformal mapping
• On the density of smooth functions in Sobolev-Orlicz spaces
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• Sobolev embeddings with variable exponent
• Sobolev embedding theorems for spaces \(W^{k,p(x)}(\Omega)\)

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