Duke Mathematical Journal

Gradient estimates for a class of parabolic systems

Emilio Acerbi and Giuseppe Mingione

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Abstract

We establish local Calderón-Zygmund-type estimates for a class of parabolic problems whose model is the nonhomogeneous, degenerate/singular parabolic $p$-Laplacian system $u_t -\operatorname{div}(|Du|^{p-2}Du) =\operatorname{div}(|F|^{p-2}F),$ proving that $F \in L_\operatorname{loc}^{ q} \Longrightarrow Du\in L^{q}_\operatorname{loc},\quad \forall\,q\geq p.$ We also treat systems with discontinuous coefficients of vanishing mean oscillation (VMO) type

Article information

Source
Duke Math. J. Volume 136, Number 2 (2007), 285-320.

Dates
First available: 21 December 2006

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1166711371

Digital Object Identifier
doi:10.1215/S0012-7094-07-13623-8

Mathematical Reviews number (MathSciNet)
MR2286632

Zentralblatt MATH identifier
1113.35105

Subjects
Primary: 35K55: Nonlinear parabolic equations
Secondary: 35K65: Degenerate parabolic equations

Citation

Acerbi, Emilio; Mingione, Giuseppe. Gradient estimates for a class of parabolic systems. Duke Mathematical Journal 136 (2007), no. 2, 285--320. doi:10.1215/S0012-7094-07-13623-8. http://projecteuclid.org/euclid.dmj/1166711371.


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