Stochastic homogenization of fully nonlinear uniformly elliptic equations revisited
Smart, Charles K.; Armstrong, Scott N. (2014), Stochastic homogenization of fully nonlinear uniformly elliptic equations revisited, Calculus of Variations and Partial Differential Equations, 50, 3-4, p. 967-980. http://dx.doi.org/10.1007/s00526-013-0663-z
TypeArticle accepté pour publication ou publié
External document linkhttp://fr.arxiv.org/abs/1209.4741
Journal nameCalculus of Variations and Partial Differential Equations
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Abstract (EN)We give a simplified presentation of the obstacle problem approach to stochastic homogenization for elliptic equations in nondivergence form. Our argument also applies to equations which depend on the gradient of the unknown function. In the latter case, we overcome difficulties caused by a lack of estimates for the first derivatives of approximate correctors by modifying the perturbed test function argument to take advantage of the spreading of the contact set.
Subjects / Keywordsfully nonlinear elliptic equation; stochastic homogenization
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Error estimates and convergence rates for the stochastic homogenization of Hamilton-Jacobi equations Armstrong, Scott N.; Cardaliaguet, Pierre; Souganidis, Panagiotis E. (2014) Article accepté pour publication ou publié