國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Quantitative stochastic homogenizati...

Armstrong, Scott.

Quantitative stochastic homogenization and large-scale regularity

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Quantitative stochastic homogenization and large-scale regularityby Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat.
作者:	Armstrong, Scott.
其他作者:	Kuusi, Tuomo.
出版者:	Cham :Springer International Publishing :2019.
面頁冊數:	xxxviii, 518 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Homogenization (Differential equations)
電子資源:	https://doi.org/10.1007/978-3-030-15545-2
ISBN:	9783030155452$q(electronic bk.)

Quantitative stochastic homogenization and large-scale regularity
Armstrong, Scott.

Quantitative stochastic homogenization and large-scale regularity[electronic resource] /by Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat. - Cham :Springer International Publishing :2019. - xxxviii, 518 p. :ill., digital ;24 cm. - Grundlehren der mathematischen wissenschaften, a series of comprehensive studies in mathematics,v.3520072-7830 ;. - Grundlehren der mathematischen wissenschaften, a series of comprehensive studies in mathematics ;345..

Preface -- 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.

The 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.

ISBN: 9783030155452$q(electronic bk.)

Standard No.: 10.1007/978-3-030-15545-2doiSubjects--Topical Terms:

308616
Homogenization (Differential equations)

LC Class. No.: QA377 / .A767 2019

Dewey Class. No.: 515.353

Quantitative stochastic homogenization and large-scale regularity
LDR:03157nmm a2200337 a 4500 001 559049
003 DE-He213
005 20191030150824.0
006 m d
007 cr nn 008maaau
008 191219s2019 gw s 0 eng d
020 $a 9783030155452$q(electronic bk.)
020 $a 9783030155445$q(paper)
024 7 $a 10.1007/978-3-030-15545-2 $2 doi
035 $a 978-3-030-15545-2
040 $a GP $c GP
041 0 $a eng
050 4 $a QA377 $b .A767 2019
072 7 $a PBKJ $2 bicssc
072 7 $a MAT007000 $2 bisacsh
072 7 $a PBKJ $2 thema
082 0 4 $a 515.353 $2 23
090 $a QA377 $b .A738 2019
100 1 $a Armstrong, Scott. $3 841923
245 1 0 $a Quantitative stochastic homogenization and large-scale regularity $h [electronic resource] / $c by Scott Armstrong, Tuomo Kuusi, Jean-Christophe Mourrat.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2019.
300 $a xxxviii, 518 p. : $b ill., digital ; $c 24 cm.
490 1 $a Grundlehren der mathematischen wissenschaften, a series of comprehensive studies in mathematics, $x 0072-7830 ; $v v.352
505 0 $a Preface -- 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.
520 $a The 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.
650 0 $a Homogenization (Differential equations) $3 308616
650 1 4 $a Partial Differential Equations. $3 274075
650 2 4 $a Probability Theory and Stochastic Processes. $3 274061
650 2 4 $a Mathematical Physics. $3 522725
650 2 4 $a Calculus of Variations and Optimal Control; Optimization. $3 274198
700 1 $a Kuusi, Tuomo. $3 841924
700 1 $a Mourrat, Jean-Christophe. $3 841925
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Grundlehren der mathematischen wissenschaften, a series of comprehensive studies in mathematics ; $v 345. $3 569154
856 4 0 $u https://doi.org/10.1007/978-3-030-15545-2
950 $a Mathematics and Statistics (Springer-11649)