Local Boundedness and Harnack Inequality for Solutions of Linear Nonuniformly Elliptic Equations

Local Boundedness and Harnack Inequality for Solutions of Linear Nonuniformly Elliptic Equations

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...

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Veröffentlicht in:Communications on pure and applied mathematics 2021-03, Vol.74 (3), p.453-477
Hauptverfasser: Bella, Peter, Schäffner, Mathias
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Applications of mathematics
Elliptic functions
Integral calculus
Integral equations
Mathematical analysis
Regularity
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description 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. © 2019 the Authors. Communications on Pure and Applied Mathematics is published by the Courant Institute of Mathematical Sciences and Wiley Periodicals, Inc.
doi_str_mv 10.1002/cpa.21876
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subjects Applications of mathematics
Elliptic functions
Integral calculus
Integral equations
Mathematical analysis
Regularity
title Local Boundedness and Harnack Inequality for Solutions of Linear Nonuniformly Elliptic Equations
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