Gradient estimates for parabolic problems with Orlicz growth and discontinuous coefficients

Oh, Jehan; Ok, Jihoon

doi:10.1002/mma.7845

Cited by 3 publications

(1 citation statement)

References 23 publications

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“…In addition, Baroni and Lindfors [2] obtained the Hölder and Lipschitz continuity of solutions to Cauchy-Dirichlet problem for parabolic equations (N = 1) with ϕ-growth. For more regularity results for the parabolic system with ϕ-growth we refer to [7,15,22,23,24,33].…”

Section: Introductionmentioning

confidence: 99%

Boundary partial regularity for minimizers of discontinuous quasiconvex integrals with general growth

Ok,

Scilla,

Stroffolini

2022

CPAA

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We prove the partial Hölder continuity on boundary points for minimizers of quasiconvex non-degenerate functionals<disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{equation*} \mathcal{F}({\mathbf u}) \colon = \int_{\Omega} f(x, {\mathbf u}, D{\mathbf u})\, \mathrm{d}x\, , \end{equation*} $\end{document} </tex-math></disp-formula>where <inline-formula><tex-math id="M1">\begin{document}$ f $\end{document}</tex-math></inline-formula> satisfies a uniform VMO condition with respect to the <inline-formula><tex-math id="M2">\begin{document}$ x $\end{document}</tex-math></inline-formula>-variable, is continuous with respect to <inline-formula><tex-math id="M3">\begin{document}$ {\mathbf u} $\end{document}</tex-math></inline-formula> and has a general growth with respect to the gradient variable.

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Section: Introductionmentioning

confidence: 99%

Boundary partial regularity for minimizers of discontinuous quasiconvex integrals with general growth

Ok,

Scilla,

Stroffolini

2022

CPAA

Self Cite

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Regularity theory for parabolic systems with Uhlenbeck structure

Ok,

Scilla,

Stroffolini

2024

Journal de Mathématiques Pures et Appliquées

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Local Calderón-Zygmund estimates for parabolic equations in weighted Lebesgue spaces

Lee

2023

MINE

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<abstract>We prove local Calderón-Zygmund type estimates for the gradient of weak solutions to degenerate or singular parabolic equations of $ p $-Laplacian type with $ p > \frac{2n}{n+2} $ in weighted Lebesgue spaces $ L^q_w $. We introduce a new condition on the weight $ w $ which depends on the intrinsic geometry concerned with the parabolic $ p $-Laplace problems. Our condition is weaker than the one in [<xref ref-type="bibr" rid="b13">13</xref>], where similar estimates were obtained. In particular, in the case $ p = 2 $, it is the same as the condition of the usual parabolic $ A_q $ weight.</abstract>

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Gradient estimates for parabolic problems with Orlicz growth and discontinuous coefficients

Abstract: We obtain Calderón-Zygmund-type estimates for parabolic equations with Orlicz growth, where nonlinearities involved in the equations may be discontinuous for the space and time variables. In addition, we consider parabolic systems with the Uhlenbeck structure.

Cited by 3 publications

References 23 publications

Boundary partial regularity for minimizers of discontinuous quasiconvex integrals with general growth

Boundary partial regularity for minimizers of discontinuous quasiconvex integrals with general growth

Regularity theory for parabolic systems with Uhlenbeck structure

Local Calderón-Zygmund estimates for parabolic equations in weighted Lebesgue spaces

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