LEADER 04692nam 22006135 450 001 9910338250103321 005 20200630145646.0 010 $a3-030-15545-5 024 7 $a10.1007/978-3-030-15545-2 035 $a(CKB)4100000008153976 035 $a(MiAaPQ)EBC5771569 035 $a(DE-He213)978-3-030-15545-2 035 $a(PPN)236522450 035 $a(EXLCZ)994100000008153976 100 $a20190509d2019 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aQuantitative Stochastic Homogenization and Large-Scale Regularity /$fby Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (548 pages) 225 1 $aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$x0072-7830 ;$v352 311 $a3-030-15544-7 327 $aPreface -- Assumptions and examples -- Frequently asked questions -- Notation -- Introduction and qualitative theory -- Convergence of the subadditive quantities -- Regularity on large scales -- Quantitative description of first-order correctors -- Scaling limits of first-order correctors -- Quantitative two-scale expansions -- Calderon-Zygmund gradient L^p estimates -- Estimates for parabolic problems -- Decay of the parabolic semigroup -- Linear equations with nonsymmetric coefficients -- Nonlinear equations -- Appendices: A.The O_s notation -- B.Function spaces and elliptic equations on Lipschitz domains -- C.The Meyers L^{2+\delta} estimate -- D. Sobolev norms and heat flow -- Parabolic Green functions -- Bibliography -- Index. 330 $aThe focus of this book is the large-scale statistical behavior of solutions of divergence-form elliptic equations with random coefficients, which is closely related to the long-time asymptotics of reversible diffusions in random media and other basic models of statistical physics. Of particular interest is the quantification of the rate at which solutions converge to those of the limiting, homogenized equation in the regime of large scale separation, and the description of their fluctuations around this limit. This self-contained presentation gives a complete account of the essential ideas and fundamental results of this new theory of quantitative stochastic homogenization, including the latest research on the topic, and is supplemented with many new results. The book serves as an introduction to the subject for advanced graduate students and researchers working in partial differential equations, statistical physics, probability and related fields, as well as a comprehensive reference for experts in homogenization. Being the first text concerned primarily with stochastic (as opposed to periodic) homogenization and which focuses on quantitative results, its perspective and approach are entirely different from other books in the literature. . 410 0$aGrundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics,$x0072-7830 ;$v352 606 $aPartial differential equations 606 $aProbabilities 606 $aMathematical physics 606 $aCalculus of variations 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aCalculus of Variations and Optimal Control; Optimization$3https://scigraph.springernature.com/ontologies/product-market-codes/M26016 615 0$aPartial differential equations. 615 0$aProbabilities. 615 0$aMathematical physics. 615 0$aCalculus of variations. 615 14$aPartial Differential Equations. 615 24$aProbability Theory and Stochastic Processes. 615 24$aMathematical Physics. 615 24$aCalculus of Variations and Optimal Control; Optimization. 676 $a515.35 676 $a515.353 700 $aArmstrong$b Scott$4aut$4http://id.loc.gov/vocabulary/relators/aut$0781700 702 $aKuusi$b Tuomo$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aMourrat$b Jean-Christophe$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910338250103321 996 $aQuantitative Stochastic Homogenization and Large-Scale Regularity$92525717 997 $aUNINA