Quantitative stochastic homogenization and large-scale regularity:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cham, Switzerland
Springer
[2019]
|
| Series: | Grundlehren der mathematischen Wissenschaften
volume 352 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Buchcover |
| Physical Description: | xxxviii, 518 Seiten Diagramme 25 cm |
| ISBN: | 9783030155445 |
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MARC
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| 245 | 1 | 0 | |a Quantitative stochastic homogenization and large-scale regularity |c Scott Armstrong ; Tuomo Kuusi ; Jean-Christophe Mourrat |
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Record in the Search Index
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| adam_text | Contents
1 Introduction and Qualitative Theory 1
11A Brief and Informal Introduction to Homogenization 1
1 2 The Subadditive Quantity ß and Its Basic Properties 5
1 3 Convergence of the Subadditive Quantity 10
1 4 Weak Convergence of Gradients and Fluxes 17
1 5 Homogenization of the Dirichlet Problem 28
2 Convergence of the Subadditive Quantities 37
2 1 The Dual Subadditive Quantity ß 38
2 2 Quantitative Convergence of the Subadditive Quantities 48
2 3 Quantitative Homogenization of the Dirichlet Problem 62
3 Regularity on Large Scales 67
3 1 Brief Review of Classical Elliptic Regularity 68
32A C01-Type Estimate 74
3 3 Higher-Order Regularity Theory and Liouville Theorems 82
3 4 The First-Order Correctors 98
3 5 Boundary Regularity 106
3 6 Optimality of the Regularity Theory 117
4 Quantitative Description of First-Order Correctors 123
4 1 The Energy Quantity J and Its Basic Properties 125
4 2 The Additive Structure of 7i 131
4 3 Improvement of Additivity 134
4 4 Localization Estimates 149
4 5 Fluctuation Estimates 163
4 6 Corrector Estimates in Weak Norms 172
4 7 Corrector Oscillation Estimates in Two Dimensions 180
xiv Contents
5 Scaling Limits of First-Order Correctors 191
5 1 White Noise and the Gaussian Free Field 191
5 2 Explicit Constructions of Random Fields 200
5 3 Heuristic Derivation of the Scaling Limit 215
54A Central Limit Theorem for J 217
5 5 Convergence of the Correctors to a Gaussian Free Field 234
6 Quantitative Two-Scale Expansions 243
6 1 The Flux Correctors 244
6 2 Quantitative Two-Scale Expansions Without Boundaries 250
6 3 Two-Scale Expansions for the Dirichlet Problem 259
6 4 Boundary Layer Estimates 266
7 Calderon-Zygmund Gradient Lp Estimates 275
7 1 Interior Calderon-Zygmund Estimates 275
7 2 Global Calderon-Zygmund Estimates 287
7 3 W ^-Type Estimates for the Two-Scale Expansion Error 293
8 Estimates for Parabolic Problems 301
8 1 Function Spaces and Some Basic Estimates 302
8 2 Homogenization of the Cauchy-Dirichlet Problem 307
83A Parabolic C0,1 -Type Estimate 314
8 4 Parabolic Higher Regularity and Liouville Theorems 319
8 5 Decay of the Green Functions and Their Gradients 320
8 6 Homogenization of the Green Functions 332
9 Decay of the Parabolic Semigroup 347
9 1 Optimal Decay of the Parabolic Semigroup 349
9 2 Homogenization of the Green Functions: Optimal Scaling 369
10 Linear Equations with Nonsymmetric Coefficients 391
10 1 Variational Formulation of General Linear Equations 392
10 2 The Double-Variable Subadditive Quantities 397
10 3 Convergence of the Subadditive Quantities 407
10 4 Quantitative Homogenization of the Dirichlet Problem 412
11 Nonlinear Equations 417
11 1 Assumptions and Preliminaries 417
11 2 Subadditive Quantities and Basic Properties 420
11 3 Convergence of the Subadditive Quantities 428
11 4 Quantitative Homogenization of the Dirichlet Problem 436
11 5 C ‘’■‘-Type Estimate 451
Contents
xv
Appenidx A: The Os Notation 455
Appendix B: Function Spaces and Elliptic Equations on Lipschitz
Domains 465
Appendix C: The Meyers L2+s Estimate 473
Appendix D: Sobolev Norms and Heat Flow 481
Appendix E: Parabolic Green Functions 499
References 511
|
| any_adam_object | 1 |
| author | Armstrong, Scott Kuusi, Tuomo Mourrat, Jean-Christophe |
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| author_sort | Armstrong, Scott |
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| building | Verbundindex |
| bvnumber | BV045954112 |
| classification_rvk | SK 540 SK 800 SK 950 |
| ctrlnum | (OCoLC)1107376121 (DE-599)BVBBV045954112 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV045954112 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:31:26Z |
| institution | BVB |
| isbn | 9783030155445 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031336149 |
| oclc_num | 1107376121 |
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| owner | DE-20 DE-703 DE-11 DE-83 DE-188 |
| owner_facet | DE-20 DE-703 DE-11 DE-83 DE-188 |
| physical | xxxviii, 518 Seiten Diagramme 25 cm |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | Springer |
| record_format | marc |
| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Armstrong, Scott (DE-588)1187679801 aut Quantitative stochastic homogenization and large-scale regularity Scott Armstrong ; Tuomo Kuusi ; Jean-Christophe Mourrat Cham, Switzerland Springer [2019] © 2019 xxxviii, 518 Seiten Diagramme 25 cm txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften volume 352 Homogenization (Differential equations) Homogenisierungsmethode (DE-588)4257770-6 gnd rswk-swf Statistische Physik (DE-588)4057000-9 gnd rswk-swf Homogenisierungsmethode (DE-588)4257770-6 s Statistische Physik (DE-588)4057000-9 s DE-604 Kuusi, Tuomo (DE-588)116302810X aut Mourrat, Jean-Christophe (DE-588)1187679623 aut Erscheint auch als Online-Ausgabe 978-3-030-15545-2 Grundlehren der mathematischen Wissenschaften volume 352 (DE-604)BV000000395 352 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031336149&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis SWB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031336149&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Buchcover |
| spellingShingle | Armstrong, Scott Kuusi, Tuomo Mourrat, Jean-Christophe Quantitative stochastic homogenization and large-scale regularity Grundlehren der mathematischen Wissenschaften Homogenization (Differential equations) Homogenisierungsmethode (DE-588)4257770-6 gnd Statistische Physik (DE-588)4057000-9 gnd |
| subject_GND | (DE-588)4257770-6 (DE-588)4057000-9 |
| title | Quantitative stochastic homogenization and large-scale regularity |
| title_auth | Quantitative stochastic homogenization and large-scale regularity |
| title_exact_search | Quantitative stochastic homogenization and large-scale regularity |
| title_full | Quantitative stochastic homogenization and large-scale regularity Scott Armstrong ; Tuomo Kuusi ; Jean-Christophe Mourrat |
| title_fullStr | Quantitative stochastic homogenization and large-scale regularity Scott Armstrong ; Tuomo Kuusi ; Jean-Christophe Mourrat |
| title_full_unstemmed | Quantitative stochastic homogenization and large-scale regularity Scott Armstrong ; Tuomo Kuusi ; Jean-Christophe Mourrat |
| title_short | Quantitative stochastic homogenization and large-scale regularity |
| title_sort | quantitative stochastic homogenization and large scale regularity |
| topic | Homogenization (Differential equations) Homogenisierungsmethode (DE-588)4257770-6 gnd Statistische Physik (DE-588)4057000-9 gnd |
| topic_facet | Homogenization (Differential equations) Homogenisierungsmethode Statistische Physik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031336149&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031336149&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
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