Local continuity and Harnack's inequality for double-phase parabolic equations

DOI10.1007/s11118-020-09879-9zbMath1481.35047OpenAlexW3094081966MaRDI QIDQ2072152

Kateryna O. Buryachenko, Igor I. Skrypnik

Publication date: 26 January 2022

Published in: Potential Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11118-020-09879-9

zbMATH Keywords

a priori estimatesHarnack's inequalitylocal continuitydouble-phase parabolic equations

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order parabolic equations (35K20) A priori estimates in context of PDEs (35B45) Quasilinear elliptic equations (35J62) Quasilinear parabolic equations with (p)-Laplacian (35K92) Quasilinear parabolic equations (35K59)

Related Items (10)

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 ⋮ Harnack's inequality for quasilinear elliptic equations with generalized Orlicz growth ⋮ Harnack inequality for the nonlocal equations with general growth ⋮ Interior continuity, continuity up to the boundary, and Harnack's inequality for double‐phase elliptic equations with nonlogarithmic conditions ⋮ Harnack's inequality for degenerate double phase parabolic equations under the non-logarithmic Zhikov's condition ⋮ Harnack inequality for solutions of the \(p(x)\)-Laplace equation under the precise non-logarithmic Zhikov's conditions ⋮ Continuity and Harnack inequalities for local minimizers of non uniformly elliptic functionals with generalized Orlicz growth under the non-logarithmic conditions ⋮ \( \mathcal{B}_1\) classes of De Giorgi-Ladyzhenskaya-Ural'tseva and their applications to elliptic and parabolic equations with generalized Orlicz growth conditions ⋮ Regularity for quasi-linear parabolic equations with nonhomogeneous degeneracy or singularity

Cites Work

• Unnamed Item
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• Parabolic equations with \(p,q\)-growth
• Parabolic systems with \({p,q}\)-growth: a variational approach
• Bounded minimisers of double phase variational integrals
• The Cauchy-Dirichlet problem for a general class of parabolic equations
• Degenerate parabolic equations
• Local clustering of the non-zero set of functions in \(W^{1,1} (E)\)
• Regularity of minimizers of integrals of the calculus of variations with non-standard growth conditions
• Hölder continuity of minimizers of functionals with non standard growth conditions
• Regularity results for quasiminima of functionals with non-polynomial growth
• On Lavrentiev's phenomenon
• Electrorheological fluids: modeling and mathematical theory
• Regularity for general functionals with double phase
• Sharp regularity for functionals with (\(p\),\(q\)) growth
• Harnack inequality for minimizers of integral functionals with general growth conditions
• Regularity for double phase variational problems
• Harnack inequalities for double phase functionals
• Regularity for parabolic systems of Uhlenbeck type with Orlicz growth
• Linear and quasilinear elliptic equations
• Pointwise estimates of solutions to the double-phase elliptic equations
• Regularity and existence of solutions of elliptic equations with p,q- growth conditions
• Harnack's Inequality for Degenerate and Singular Parabolic Equations
• Harnack estimates for weak supersolutions to nonlinear degenerate parabolic equations
• H\"{o}lder continuity of a bounded weak solution of generalized parabolic $p-$Laplacian equations
• A new proof of the Hölder continuity of solutions to p-Laplace type parabolic equations
• Some remarks on the regularity of minima of anisotropic integrals
• The natural generalizationj of the natural conditions of ladyzhenskaya and uralľtseva for elliptic equations
• PARABOLIC EQUATIONS WITH p,q-GROWTH: THE SUBQUADRATIC CASE

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