Hölder continuity of solutions of parabolic equations with variable nonlinearity exponent

DOI10.1007/s10958-011-0599-9zbMath1291.35110OpenAlexW2010804951MaRDI QIDQ2248985

Yury A. Alkhutov, Vasilii V. Jikov

Publication date: 27 June 2014

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-011-0599-9

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear parabolic equations (35K55)

Related Items (15)

On the weak Harnack inequality for the parabolic p ( x )-Laplacian ⋮ Regularity for parabolic equations with time dependent growth ⋮ 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 ⋮ Unnamed Item ⋮ On the continuity of solutions of the nonhomogeneous evolution \(p(x, t)\)-Laplace equation ⋮ Parabolic Harnack estimates for anisotropic slow diffusion ⋮ Harnack's inequality for degenerate double phase parabolic equations under the non-logarithmic Zhikov's condition ⋮ \( {\mathfrak{B}}_1\) classes of De Giorgi, Ladyzhenskaya, and Ural'tseva and their application to elliptic and parabolic equations with nonstandard growth ⋮ Higher regularity of solutions of singular parabolic equations with variable nonlinearity ⋮ Global estimates for solutions of singular parabolic and elliptic equations with variable nonlinearity ⋮ On the continuity of solutions to doubly singular parabolic equations ⋮ Local continuity of singular anisotropic parabolic equations with variable growth ⋮ Harnack's inequality of weak type for the parabolic \(p (x)\)-Laplacian

Cites Work

• Degenerate parabolic equations
• On Lavrentiev's phenomenon
• On some variational problems
• Regularity results for parabolic systems related to a class of non-Newtonian fluids.
• Higher integrability for parabolic equations of \(p(x,t)\)-Laplacian type
• Continuity at boundary points of solutions of quasilinear elliptic equations with a non-standard growth condition
• ELLIPTIC PROBLEMS WITH A PARAMETER AND PARABOLIC PROBLEMS OF GENERAL TYPE
• Regularity results for a class of functionals with non-standard growth
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