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

Abstract

Under appropriate assumptions on the $N(\hat{I}\text{c◯})$-fucntion, the $L^{\hat{I}¦(A(x,\cdot ))}$ 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