We study local regularity properties for solutions of linear, non-uniformly elliptic equations. Assuming certain integrability conditions on the coefficient field, we prove local boundedness and Harnack inequality. The assumed integrability assumptions are essentially sharp and improve upon classical results by Trudinger [ARMA 1971]. We then apply the deterministic regularity results to the corrector equation in stochastic homogenization and establish sublinearity of the corrector.

中文翻译：

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线性非均匀椭圆方程解的局部有界和哈纳克不等式

我们研究了线性非均匀椭圆方程解的局部正则性。假设系数场具有一定的可积性条件，我们证明了局部有界性和 Harnack 不等式。假设的可积性假设本质上是尖锐的，并且改进了 Trudinger [ARMA 1971] 的经典结果。然后，我们将确定性规律结果应用于随机均质化中的校正器方程，并建立校正器的亚线性。