Gradient regularity via rearrangements for $p$-Laplacian type elliptic boundary value problems

Cianchi, Andrea, and Maz'ya, Vladimir G.. "Gradient regularity via rearrangements for $p$-Laplacian type elliptic boundary value problems." Journal of the European Mathematical Society 016.3 (2014): 571-595. <http://eudml.org/doc/277686>.

@article{Cianchi2014,
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.},
author = {Cianchi, Andrea, Maz'ya, Vladimir G.},
journal = {Journal of the European Mathematical Society},
keywords = {nonlinear elliptic equations; Dirichlet problems; Neumann problems; gradient estimates; rearrangements; Lorentz spaces; Orlicz spaces; Hardy-type inequalities; gradient estimates; Dirichlet problems; Neumann problems; Lorentz spaces; Orlicz spaces; Hardy-type inequalities},
language = {eng},
number = {3},
pages = {571-595},
publisher = {European Mathematical Society Publishing House},
title = {Gradient regularity via rearrangements for $p$-Laplacian type elliptic boundary value problems},
url = {http://eudml.org/doc/277686},
volume = {016},
year = {2014},
}

TY - JOUR
AU - Cianchi, Andrea
AU - Maz'ya, Vladimir G.
TI - Gradient regularity via rearrangements for $p$-Laplacian type elliptic boundary value problems
JO - Journal of the European Mathematical Society
PY - 2014
PB - European Mathematical Society Publishing House
VL - 016
IS - 3
SP - 571
EP - 595
AB - 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.
LA - eng
KW - nonlinear elliptic equations; Dirichlet problems; Neumann problems; gradient estimates; rearrangements; Lorentz spaces; Orlicz spaces; Hardy-type inequalities; gradient estimates; Dirichlet problems; Neumann problems; Lorentz spaces; Orlicz spaces; Hardy-type inequalities
UR - http://eudml.org/doc/277686
ER -