Journal
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
Volume 74, Issue 3, Pages 453-477Publisher
WILEY
DOI: 10.1002/cpa.21876
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Funding
- Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) [313878761]
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In this study, we investigate the local regularity properties of solutions of linear, nonuniformly elliptic equations by assuming certain integrability conditions on the coefficient field. We prove local boundedness and Harnack inequality, and apply the deterministic regularity results to the corrector equation in stochastic homogenization, establishing sublinearity of the corrector.
We study local regularity properties for solutions of linear, nonuniformly 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. We then apply the deterministic regularity results to the corrector equation in stochastic homogenization and establish sublinearity of the corrector. (c) 2019 the Authors. Communications on Pure and Applied Mathematics is published by the Courant Institute of Mathematical Sciences and Wiley Periodicals, Inc.
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