多相椭圆问题的局部高阶可积性

Local higher integrability of multi-phase elliptic problems

为了研究Musielak Orlicz Sobolev空间上与多相泛函相对应的非一致椭圆方程,给出适当的检验函数,利用Young不等式、Sobolev Poincaré不等式、Gehring引理等,建立解的Caccioppoli不等式和逆H lder不等式,进而获得解的局部高阶可积性。

In order to consider the non-uniform elliptic equation corresponding to the multi-phase functional on Musielak Orlicz Sobolev space,Caccioppoli inequality and reverse H lder inequality are established to obtain the local higher integrability of its solution by using an appropriate test function,Young inequality,Sobolev Poincaréinequality and Gehring lemma.