Regularity of scalar elliptic equation by Moser iteration

Theorem Suppose {v \in W^{1,2}(B_R)} is a subsolution of {-\partial_i (a^{ij}(x) \partial_j u) =0}, {\lambda I \le (a^{ij}(x)) \le \Lambda I}. Then for all {p>0}, {0<\theta <1},

\displaystyle \sup_{B_{\theta R}} v \le C(n, \lambda, \Lambda, p) (1- \theta)^{- \frac{n}{p}} \left( \frac{1}{|B_R|} \int_{B_R} (v^+)^p \right)^{\frac{1}{p}}.

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