Periodic homogenization of elliptic systems /
Saved in:
| Author / Creator: | Shen, Zhongwei, 1963- author. |
|---|---|
| Imprint: | Cham, Switzerland : Birkhäuser, 2018. |
| Description: | 1 online resource |
| Language: | English |
| Series: | Operator theory: advances in applications, 2504-3587 ; volume 269 Operator theory, advances and applications ; v. 269. |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/11705971 |
MARC
| LEADER | 00000cam a2200000Ii 4500 | ||
|---|---|---|---|
| 001 | 11705971 | ||
| 005 | 20210625185132.5 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 180914s2018 sz ob 001 0 eng d | ||
| 019 | |a 1052872384 | ||
| 020 | |a 9783319912141 |q (electronic bk.) | ||
| 020 | |a 3319912143 |q (electronic bk.) | ||
| 020 | |z 9783319912134 |q (print) | ||
| 020 | |z 3319912135 | ||
| 035 | |a (OCoLC)1052566500 |z (OCoLC)1052872384 | ||
| 035 | 9 | |a (OCLCCM-CC)1052566500 | |
| 040 | |a N$T |b eng |e rda |e pn |c N$T |d GW5XE |d N$T |d EBLCP |d YDX |d OCLCF |d FIE |d UAB |d OTZ |d LVT |d U3W |d CAUOI |d LEAUB |d MERER |d ESU |d COO |d LQU |d LIP |d LEATE |d OCLCQ |d SFB |d U@J |d OCLCQ | ||
| 049 | |a MAIN | ||
| 050 | 4 | |a QA377 | |
| 066 | |c (S | ||
| 072 | 7 | |a MAT |x 005000 |2 bisacsh | |
| 072 | 7 | |a MAT |x 034000 |2 bisacsh | |
| 100 | 1 | |a Shen, Zhongwei, |d 1963- |e author. |0 http://id.loc.gov/authorities/names/n91088084 | |
| 245 | 1 | 0 | |a Periodic homogenization of elliptic systems / |c Zhongwei Shen. |
| 264 | 1 | |a Cham, Switzerland : |b Birkhäuser, |c 2018. | |
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Operator theory: advances in applications, |x 2504-3587 ; |v volume 269 | |
| 504 | |a Includes bibliographical references and index. | ||
| 588 | 0 | |a Online resource; title from PDF title page (SpringerLink, viewed September 17, 2018). | |
| 505 | 0 | |a Intro; Contents; Preface; Chapter 1 Introduction; 1.1 Homogenization theory; 1.2 General presentation of the monograph; Qualitative homogenization theory; Convergence rates; Interior and boundary regularity estimates; The problem of convergence rates revisited; L2 boundary value problems in Lipschitz domains; 1.3 Readership; 1.4 Notation; Chapter 2 Second-Order Elliptic Systems with Periodic Coefficients; 2.1 Weak solutions; 2.2 Two-scale asymptotic expansions and the homogenized operator; Correctors and effective coefficients; 2.3 Homogenization of elliptic systems | |
| 505 | 8 | |a 6.4 Boundary Lipschitz estimates6.5 Matrix of Neumann functions; 6.6 Elliptic systems of linear elasticity; 6.7 Notes; Chapter 7 Convergence Rates, Part II; 7.1 Convergence rates in H1 and L2; 7.2 Convergence rates of eigenvalues; 7.3 Asymptotic expansions of Green functions; 7.4 Asymptotic expansions of Neumann functions; 7.5 Convergence rates in Lp and W1,p; 7.6 Notes; Chapter 8 L2 Estimates in Lipschitz Domains; 8.1 Lipschitz domains and nontangential convergence; 8.2 Estimates of fundamental solutions; 8.3 Estimates of singular integrals; 8.4 The method of layer potentials | |
| 505 | 8 | |a 8.5 Laplace's equation8.6 The Rellich property; 8.7 The well-posedness for the small scale; 8.8 Rellich estimates for the large scale; 8.9 L2 boundary value problems; 8.10 L2 estimates in arbitrary Lipschitz domains; 8.11 Square function and H1/2 estimates; 8.12 Notes; Bibliography; Index | |
| 520 | |a This monograph surveys the theory of quantitative homogenization for second-order linear elliptic systems in divergence form with rapidly oscillating periodic coefficients in a bounded domain. It begins with a review of the classical qualitative homogenization theory, and addresses the problem of convergence rates of solutions. The main body of the monograph investigates various interior and boundary regularity estimates that are uniform in the small parameter e>0. Additional topics include convergence rates for Dirichlet eigenvalues and asymptotic expansions of fundamental solutions, Green functions, and Neumann functions. The monograph is intended for advanced graduate students and researchers in the general areas of analysis and partial differential equations. It provides the reader with a clear and concise exposition of an important and currently active area of quantitative homogenization.-- |c Provided by publisher. | ||
| 650 | 0 | |a Homogenization (Differential equations) |0 http://id.loc.gov/authorities/subjects/sh92002059 | |
| 650 | 0 | |a Differential equations, Elliptic |x Numerical solutions. |0 http://id.loc.gov/authorities/subjects/sh85037897 | |
| 650 | 1 | 4 | |a Partial Differential Equations. |0 http://scigraph.springernature.com/things/product-market-codes/M12155 |
| 650 | 2 | 4 | |a Probability Theory and Stochastic Processes. |0 http://scigraph.springernature.com/things/product-market-codes/M27004 |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Differential equations, Elliptic |x Numerical solutions. |2 fast |0 (OCoLC)fst00893461 | |
| 650 | 7 | |a Homogenization (Differential equations) |2 fast |0 (OCoLC)fst00959714 | |
| 655 | 4 | |a Electronic books. | |
| 776 | 0 | 8 | |i Print version: |a Shen, Zhongwei, 1963- |t Periodic homogenization of elliptic systems. |d Cham, Switzerland : Birkhäuser, 2018 |z 3319912135 |z 9783319912134 |w (OCoLC)1030911120 |
| 830 | 0 | |a Operator theory, advances and applications ; |v v. 269. |0 http://id.loc.gov/authorities/names/n42017868 | |
| 880 | 8 | |6 505-00/(S |a 4.2 A real-variable method4.3 Interior W1,p estimates; 4.4 Asymptotic expansions of fundamental solutions; 4.5 Notes; Chapter 5 Regularity for the Dirichlet Problem; 5.1 Boundary localization in the periodic setting; 5.2 Boundary Hölder estimates; 5.3 Boundary W1,p estimates; 5.4 Green functions and Dirichlet correctors; 5.5 Boundary Lipschitz estimates; 5.6 The Dirichlet problem in C1 and C1,α domains; 5.7 Notes; Chapter 6 Regularity for the Neumann Problem; 6.1 Approximation of solutions at the large scale; 6.2 Boundary Hölder estimates; 6.3 Boundary W1,p estimates | |
| 880 | 8 | |6 505-00/(S |a Homogenization of the Dirichlet Problem (2.1.14). Homogenization of the Neumann Problem (2.1.15).; 2.4 Elliptic systems of linear elasticity; 2.5 Notes; Chapter 3 Convergence Rates, Part I; 3.1 Flux correctors and ε-smoothing; 3.2 Convergence rates in H1 for the Dirichlet problem; 3.3 Convergence rates in H1 for the Neumann problem; 3.4 Convergence rates in Lp for the Dirichlet problem; 3.5 Convergence rates in Lp for the Neumann problem; 3.6 Convergence rates for elliptic systems of elasticity; 3.7 Notes; Chapter 4 Interior Estimates; 4.1 Interior Lipschitz estimates; A Liouville property | |
| 903 | |a HeVa | ||
| 929 | |a oclccm | ||
| 999 | f | f | |i 2c374859-a45c-5b2e-9d41-ce0e50c11dd3 |s e486484a-dd1e-5a82-8d51-4063321a951e |
| 928 | |t Library of Congress classification |a QA377 |l Online |c UC-FullText |u https://link.springer.com/10.1007/978-3-319-91214-1 |z Springer Nature |g ebooks |i 12556771 | ||