Geodesic
Gradient regularity via rearrangements for $p$-Laplacian type elliptic boundary value problems
Journal of the European Mathematical Society, Tome 16 (2014) no. 3, pp. 571-595

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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.
DOI : 10.4171/jems/440
Classification : 35-XX, 00-XX
Keywords: Nonlinear elliptic equations, Dirichlet problems, Neumann problems, gradient estimates, rearrangements, Lorentz spaces, Orlicz spaces 
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     author = {Andrea Cianchi and Vladimir G. Maz'ya},
     title = {Gradient regularity via rearrangements for $p${-Laplacian} type elliptic boundary value problems},
     journal = {Journal of the European Mathematical Society},
     pages = {571--595},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {2014},
     doi = {10.4171/jems/440},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/440/}
}
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Andrea Cianchi; Vladimir G. Maz'ya. Gradient regularity via rearrangements for $p$-Laplacian type elliptic boundary value problems. Journal of the European Mathematical Society, Tome 16 (2014) no. 3, pp. 571-595. doi: 10.4171/jems/440

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