$L^{Φ(A(x,\cdot))}$ estimate for the gradient in $W^{1,A(x,\cdot)}$

Duchao Liu; Beibei Wang; Sibei Yang

paper

$L^{Φ (A (x, \cdot))}$ estimate for the gradient in $W^{1, A (x, \cdot)}$

arXiv:1805.11469

Abstract

Under appropriate assumptions on the $N (Ω)$ -fucntion, the $L^{Φ (A (x, \cdot))}$ estimate for the gradient of the minimizers of a class of energy functional in Musielak-Orlicz-Sobolev space $W^{1, A (x, \cdot)}$ is presented by using Calderón-Zygmund decomposition.

31 pages. arXiv admin note: text overlap with arXiv:1711.11229

LΦ(A(x,⋅)) estimate for the gradient in W1,A(x,⋅)

Abstract

$L^{Φ (A (x, \cdot))}$ estimate for the gradient in $W^{1, A (x, \cdot)}$