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- Cianchi, Andrea, et al.
(författare)
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Gradient regularity via rearrangements for p-Laplacian type elliptic boundary value problems
- 2014
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Ingår i: Journal of the European Mathematical Society (Print). - : European Mathematical Society. - 1435-9855 .- 1435-9863. ; 16:3, s. 571-595
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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