Wolff potential estimates for elliptic equations with nonstandard growth and applications

Teemu Lukkari, Fumi-Yuki Maeda, Niko Marola
2010 Forum mathematicum  
We study superharmonic functions related to elliptic equations with structural conditions involving a variable growth exponent. We establish pointwise estimates for such functions in terms of a Wolff type potential. We apply these estimates to prove a variable exponent version of the Hedberg-Wolff theorem on the dual of Sobolev spaces with zero boundary values. 2000 Mathematics Subject Classification. 35J60, 46E35, 31C45.
doi:10.1515/forum.2010.057 fatcat:ol35ykft65fppppipffofybpve