自然增长条件下障碍问题弱解的正则性

Regularity of weak solutions for obstacle problems with natural growth

研究自然增长条件下非齐次A-调和方程障碍问题弱解的正则性。首先通过证明方程障碍问题弱解的Caccippoli不等式,得到其逆Holder不等式,其次利用Gehring引理得到其局部可积性,最后利用本质零点及相关性质得到了其零点性质。

The regularity of weak solutions of obstacle problem for nonhomogeneous A-harmonic equations on natural growth are studied.By proving the Caccippoli inequality of weak solution for the obstacle problem of this equation,inverse Holder inequality is deduced and Gehring lemma is used to prove its local integrability.Finally,the properties at zero are deduced by using the essential zero properties.