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2011 Higher integrability for parabolic systems with non-standard growth and degenerate diffusions
Verena Bögelein, Frank Duzaar
Publ. Mat. 55(1): 201-250 (2011).

Abstract

The aim of this paper is to establish a Meyer's type higher integrability result for weak solutions of possibly degenerate parabolic systems of the type

$$ \partial_t u - \operatorname{div} a(x,t,Du)= \operatorname{div} \bigl(|F|^{p(x,t)-2}F\bigr).$$

The vector-field $a$ is assumed to fulfill a non-standard $p(x,t)$-growth condition. In particular it is shown that there exists $\varepsilon >0$ depending only on the structural data such that there holds:

$$|Du|^{p(\cdot)(1+\varepsilon)}\in L^1_{\operatorname{loc}},$$

together with a local estimate for the $p(\cdot)(1+\varepsilon)$-energy.

Citation

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Verena Bögelein. Frank Duzaar. "Higher integrability for parabolic systems with non-standard growth and degenerate diffusions." Publ. Mat. 55 (1) 201 - 250, 2011.

Information

Published: 2011
First available in Project Euclid: 25 February 2011

zbMATH: 1213.35148
MathSciNet: MR2779582

Subjects:
Primary: 35D10, 35K40, 35K65

Rights: Copyright © 2011 Universitat Autònoma de Barcelona, Departament de Matemàtiques

JOURNAL ARTICLE
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Vol.55 • No. 1 • 2011
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