Calderón-Zygmund estimates for parabolic \(p(x,t)\)-Laplacian systems

DOI10.4171/RMI/817zbMath1316.35160MaRDI QIDQ2256076

Verena Bögelein, Paolo Baroni

Publication date: 19 February 2015

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

zbMATH Keywords

parabolic \(p\)-Laplaciangradient estimatesnonstandard growth conditiondegenerate parabolic systems

Mathematics Subject Classification ID

Degenerate parabolic equations (35K65) Weak solutions to PDEs (35D30) Second-order parabolic systems (35K40) Singular parabolic equations (35K67) Quasilinear parabolic equations with (p)-Laplacian (35K92)

Related Items (46)

Regularity for parabolic equations with time dependent growth ⋮ An end point Orlicz type estimate for nonlinear elliptic equations ⋮ Global Lorentz estimates with variable power to linear parabolic integro-differential equations ⋮ Global gradient estimates for nonlinear obstacle problems with nonstandard growth ⋮ Harnack's inequality for singular parabolic equations with generalized Orlicz growth under the non-logarithmic Zhikov's condition ⋮ Weighted Lorentz estimate for asymptotically regular parabolic equations of \(p(x, t)\)-Laplacian type ⋮ On the continuity of solutions of quasilinear parabolic equations with generalized Orlicz growth under non-logarithmic conditions ⋮ Lorentz estimates for degenerate and singular evolutionary systems ⋮ Global a priori bounds for weak solutions to quasilinear parabolic equations with nonstandard growth ⋮ Unnamed Item ⋮ Global weighted estimates for the nonlinear parabolic equations with non-standard growth ⋮ Very weak solutions of subquadratic parabolic systems with non-standard \(p(x, t)\)-growth ⋮ Regularity estimates for the parabolic \(p (x, t)\)-Laplacian equation in Besov spaces ⋮ Global Calderón-Zygmund estimates for a class of nonlinear elliptic equations with Neumann data ⋮ Hölder estimates for the elliptic p(x)-Laplacian equation with the logarithmic function ⋮ Global gradient estimates for parabolic equations with measurable nonlinearities ⋮ Gradient estimates for the p-Laplacian parabolic equations with a low-order term ⋮ \(W^{2,p(\cdot )}\)-regularity for elliptic equations in nondivergence form with BMO coefficients ⋮ Weighted \(L^{q ( \cdot )}\)-estimates for the nonlinear parabolic equations with non-standard growth ⋮ Weighted Lorentz estimates for parabolic equations with non-standard growth on rough domains ⋮ Lorentz estimates for a class of nonlinear parabolic systems ⋮ Calderón-Zygmund estimates for nonlinear parabolic equations with matrix weights on nonsmooth domains ⋮ Harnack's inequality for degenerate double phase parabolic equations under the non-logarithmic Zhikov's condition ⋮ Survey on gradient estimates for nonlinear elliptic equations in various function spaces ⋮ Higher integrability for solutions to parabolic problems with irregular obstacles and nonstandard growth ⋮ Local Calderón-Zygmund estimates for parabolic equations in weighted Lebesgue spaces ⋮ Approximation of elliptic and parabolic equations with Dirichlet boundary conditions ⋮ \( {\mathfrak{B}}_1\) classes of De Giorgi, Ladyzhenskaya, and Ural'tseva and their application to elliptic and parabolic equations with nonstandard growth ⋮ Interior gradient estimate for steady flows of electrorheological fluids ⋮ Weighted \(L^{p(\cdot)}\)-regularity for fully nonlinear parabolic equations ⋮ Sharp gradient estimates for quasilinear elliptic equations with \(p(x)\) growth on nonsmooth domains ⋮ Compact embedding for \(p(x,t)\)-Sobolev spaces and existence theory to parabolic equations with \(p(x,t)\)-growth ⋮ Singular parabolic equations, measures satisfying density conditions, and gradient integrability ⋮ Lorentz estimate with a variable power for parabolic obstacle problems with non-standard growths ⋮ Lipschitz regularity for viscosity solutions to parabolic \({p(x,t)}\)-Laplacian equations on Riemannian manifolds ⋮ On \(W^{1,q(\cdot)}\)-estimates for elliptic equations of \(p(x)\)-Laplacian type ⋮ Lorentz estimates to nonlinear elliptic obstacle problems of \(p(x)\)-growth in Reifenberg domains ⋮ Lorentz estimate for nonlinear parabolic obstacle problems with asymptotically regular nonlinearities ⋮ End point gradient estimates for quasilinear parabolic equations with variable exponent growth on nonsmooth domains ⋮ Hessian estimates for nondivergence parabolic and elliptic equations with partially BMO coefficients ⋮ Nonlinear Parabolic Equations with Variable Exponent Growth in Nonsmooth Domains ⋮ \(L^{p(\cdot)}\)-regularity of Hessian for nondivergence parabolic and elliptic equations with measurable coefficients ⋮ Higher integrability result for nonlinear elliptic systems with conormal boundary conditions ⋮ Gradient estimates for the p(x)-Laplacian equation in R^N ⋮ Nondivergence parabolic equations in weighted variable exponent spaces ⋮ Global higher integrability for symmetric \(p(x, t)\)-Laplacian system

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