LOCAL GRADIENT ESTIMATES FOR THE p(x)-LAPLACIAN ELLIPTIC EQUATIONS

作者：Yao, Fengping^*

来源：Mathematical Inequalities & Applications, 2014, 17(1): 259-268.

DOI：10.7153/mia-17-21

• Regularity
• L-q
• divergence
• quasilinear
• elliptic
• p(x)-Laplacian

In this paper we give a new and direct proof of local L-q estimates for the nonhomogeneous p(x)-Laplacian elliptic equation under some proper conditions on p(x) > 1. We prove that
vertical bar f vertical bar(p(x)) is an element of L-loc(q) double right arrow vertical bar del(u)vertical bar(p(x)) is an element of L-loc(q) for any q >= 1
for weak solutions of
div (vertical bar del(u)vertical bar(p(x)-2)del(u)) = div (vertical bar f vertical bar(p( x)-2)f) in Omega.

• 出版日期2014-1
• 单位上海大学