We review some recent results in quantitative stochastic homogenization for divergence-form, quasilinear elliptic equations. In particular, we are interested in obtaining -type bounds on the gradient of solutions and thus giving a demonstration of the principle that solutions of equations with random coefficients have much better regularity (with overwhelming probability) than a general equation with non-constant coefficients.
@incollection{JEDP_2014____A1_0, author = {Scott Armstrong}, title = {Uniform {Lipschitz} estimates in stochastic homogenization}, booktitle = {}, series = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {1}, pages = {1--11}, publisher = {Groupement de recherche 2434 du CNRS}, year = {2014}, doi = {10.5802/jedp.104}, language = {en}, url = {https://proceedings.centre-mersenne.org/articles/10.5802/jedp.104/} }
TY - JOUR AU - Scott Armstrong TI - Uniform Lipschitz estimates in stochastic homogenization JO - Journées équations aux dérivées partielles PY - 2014 SP - 1 EP - 11 PB - Groupement de recherche 2434 du CNRS UR - https://proceedings.centre-mersenne.org/articles/10.5802/jedp.104/ DO - 10.5802/jedp.104 LA - en ID - JEDP_2014____A1_0 ER -
%0 Journal Article %A Scott Armstrong %T Uniform Lipschitz estimates in stochastic homogenization %J Journées équations aux dérivées partielles %D 2014 %P 1-11 %I Groupement de recherche 2434 du CNRS %U https://proceedings.centre-mersenne.org/articles/10.5802/jedp.104/ %R 10.5802/jedp.104 %G en %F JEDP_2014____A1_0
Scott Armstrong. Uniform Lipschitz estimates in stochastic homogenization. Journées équations aux dérivées partielles (2014), article no. 1, 11 p. doi : 10.5802/jedp.104. https://proceedings.centre-mersenne.org/articles/10.5802/jedp.104/
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