Local Boundedness and Harnack Inequality for Solutions of Linear Nonuniformly Elliptic Equations
By Peter Bella, Mathias Schäffner. Communications on Pure and Applied Mathematics, 2019
64 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mechanics of Materials
View Paper: https://www.semanticscholar.org/paper/b43cd5d0a2df4682e15f09c6d4fe0062e383c7b3
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In Applied Mathematics
- Cristiana De Filippis
- Giuseppe Mingione
- Vicentiu D. Rădulescu
- Patrick Winkert
- Frank Duzaar
- Paolo Baroni
- Verena Bogelein
- Jan Kristensen
In Computational Theory and Mathematics
- Cristiana De Filippis
- Giuseppe Mingione
- Patrick Winkert
- Vicentiu D. Rădulescu
- Frank Duzaar
- Jan Kristensen
- Verena Bogelein
- Paolo Baroni
In Mechanics of Materials
Citations in the corpus
- Regularity for Double Phase Problems at Nearly Linear Growth (2023, background): “We recall that general nonuniformly elliptic problems have been the object of intensive investigation over the last two decades [7,9–14, 33], starting from the more guarantees the local Hölder continuity of the gradient of minima of (1.3) [5,18,21].”