Regularity Of Solution For A Class Of Elliptic Equation With Nonstandard Growth

Since the last century,the regularity theory,as an important direction of partial differential equation,has been developing rapidly.In recent years,the subject of differential equation with nonstandard growth has gained more and more scholars' attention,due mainly to appearing of more and more non-linear problems,and the regularity problems are the focus of many scholars.In this paper,we will consider the regularity of weak solution to the following equation based on Orlicz-Sobolev where ?(?),A(x,z)=|z| p(x)-2z + a(x)|z|q(x)-2z,p(x),q(x)?(1,?),and a(·),F are given functions.If ?(?)RN is a bounded domain,we can get that(?)?>1 H(x,F)?Lloc?(?)(?)H(x,Du)?Lloc?(?),by using Vitali's covering theorem with some comparison estimates.If ? = RN,we have that(?)?>1?RN[H(x,Du)]?dx ? c?RN[H(x,F)]?dx?by employing the maximal function technique,the Gehring type lemma,etc.