Calderon-Zygmund type estimates for a class of obstacle problems with p(x) growth

Eleuteri M, Habermann J (2010)

Publication Type: Journal article

Publication year: 2010

Journal

Journal of Mathematical Analysis and Applications Elsevier

Publisher: Elsevier

Book Volume: 372

Pages Range: 140-161

DOI: 10.1016/j.jmaa.2010.05.072

Abstract

For local minimizers u∈Wloc ^1,p(·)(Ω) of quasiconvex integral functionals of the type. F[u]:=∫ωf(x,Du(x))dx with p(x) growth in the class K:={u∈Wloc ^1,p(·)(ω):u > Ψ}, where Ψ∈Wloc ^1,p(·)(ω) is a given obstacle function, we show estimates of Calderón-Zygmund type, i.e.|DΨ|^p(·)∈Lloc ^q⇒|Du|^p(·)∈Lloc ^q, for any q>1, provided that the modulus of continuity ω of the exponent function p satisfies the condition. ω(ρ)log1ρ→0 as ρ→0. © 2010 Elsevier Inc.

Authors with CRIS profile

Jens Habermann

Involved external institutions

Università degli Studi di Firenze / University of Florence

Italy (IT)

How to cite

APA:

Eleuteri, M., & Habermann, J. (2010). Calderon-Zygmund type estimates for a class of obstacle problems with p(x) growth. Journal of Mathematical Analysis and Applications, 372, 140-161. https://dx.doi.org/10.1016/j.jmaa.2010.05.072

MLA:

Eleuteri, Michela, and Jens Habermann. "Calderon-Zygmund type estimates for a class of obstacle problems with p(x) growth." Journal of Mathematical Analysis and Applications 372 (2010): 140-161.

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