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Calderon-Zygmund estimates for parabolic p(x, t)-Laplacian systems
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2014 (English)In: Revista matemática iberoamericana, ISSN 0213-2230, E-ISSN 2235-0616, Vol. 30, no 4, 1355-1386 p.Article in journal (Refereed) Published
Abstract [en]

We prove local Calderon-Zygmund estimates for weak solutions of the evolutionary p(x, t)-Laplacian system partial derivative(t)u - div (a(x, t)vertical bar Du vertical bar(p(x,t)-2)Du) = div (vertical bar F vertical bar F-p(x,F-t)-2 under the classical hypothesis of logarithmic continuity for the variable exponent p(x, t). More precisely, we show that the spatial gradient Du of the solution is as integrable as the right-hand side F, i.e., vertical bar F vertical bar(p(.)) is an element of L-loc(q) double right arrow vertical bar Du vertical bar(p(.)) is an element of L-loc(q) for any q > 1, together with quantitative estimates. Thereby we allow the presence of eventually discontinuous coefficients a(x, t), requiring only a VMO condition with respect to the spatial variable x.

Place, publisher, year, edition, pages
2014. Vol. 30, no 4, 1355-1386 p.
Keyword [en]
Gradient estimates, degenerate parabolic systems, nonstandard growth condition, parabolic p-Laplacian
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-252062DOI: 10.4171/RMI/817ISI: 000351974400009OAI: oai:DiVA.org:uu-252062DiVA: diva2:808698
Available from: 2015-04-29 Created: 2015-04-28 Last updated: 2017-12-04Bibliographically approved

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