论文标题
注意基本不平等及其对$ p $ harmonic功能的规律性的应用
Note on an elementary inequality and its application to the regularity of $p$-harmonic functions
论文作者
论文摘要
我们研究$ p $ harmonic功能的Sobolev规律性。我们表明，$ | du |^{\ frac {p-2+s} {2}} du $属于Sobolev Space $ W^{1,2} _ {loc} $，$ s> -1-1- \ frac {p-1} {p-1} {n-1} {n-1} {N-1} {证明是基于基本不平等的。
We study the Sobolev regularity of $p$-harmonic functions. We show that $|Du|^{\frac{p-2+s}{2}}Du$ belongs to the Sobolev space $W^{1,2}_{loc}$, $s>-1-\frac{p-1}{n-1}$, for any $p$-harmonic function $u$. The proof is based on an elementary inequality.
