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Gradient regularity via rearrangements for p-Laplacian type elliptic boundary value problems
University of Florence, Italy .
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
2014 (English)In: Journal of the European Mathematical Society (Print), ISSN 1435-9855, E-ISSN 1435-9863, Vol. 16, no 3, 571-595 p.Article in journal (Refereed) Published
Abstract [en]

A sharp estimate for the decreasing rearrangement of the length of the gradient of solutions to a class of nonlinear Dirichlet and Neumann elliptic boundary value problems is established under weak regularity assumptions on the domain. As a consequence, the problem of gradient bounds in norms depending on global integrability properties is reduced to one-dimensional Hardy-type inequalities. Applications to gradient estimates in Lebesgue, Lorentz, Zygmund, and Orlicz spaces are presented.

Place, publisher, year, edition, pages
European Mathematical Society , 2014. Vol. 16, no 3, 571-595 p.
Keyword [en]
Nonlinear elliptic equations; Dirichlet problems; Neumann problems; gradient estimates; rearrangements; Lorentz spaces; Orlicz spaces
National Category
Natural Sciences
URN: urn:nbn:se:liu:diva-105429DOI: 10.4171/JEMS/440ISI: 000331328800004OAI: diva2:706627
Available from: 2014-03-21 Created: 2014-03-21 Last updated: 2014-03-21

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Maz´ya, Vladimir
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Mathematics and Applied MathematicsThe Institute of Technology
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