Quantitative Stochastic Homogenization of Elliptic Equations in Nondivergence Form
We introduce a new method for studying stochastic homogenization of elliptic equations in nondivergence form. The main application is an algebraic error estimate, asserting that deviations from the homogenized limit are at most proportional to a power of the microscopic length scale, assuming a fini...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Springer Berlin Heidelberg
2016
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| Online Access: | http://hdl.handle.net/1721.1/105198 |
| _version_ | 1811070429847093248 |
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| author | Armstrong, Scott N. Smart, Charles |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Armstrong, Scott N. Smart, Charles |
| author_sort | Armstrong, Scott N. |
| collection | MIT |
| description | We introduce a new method for studying stochastic homogenization of elliptic equations in nondivergence form. The main application is an algebraic error estimate, asserting that deviations from the homogenized limit are at most proportional to a power of the microscopic length scale, assuming a finite range of dependence. The results are new even for linear equations. The arguments rely on a new geometric quantity which is controlled in part by adapting elements of the regularity theory for the Monge–Ampère equation. |
| first_indexed | 2024-09-23T08:35:53Z |
| format | Article |
| id | mit-1721.1/105198 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:35:53Z |
| publishDate | 2016 |
| publisher | Springer Berlin Heidelberg |
| record_format | dspace |
| spelling | mit-1721.1/1051982024-06-26T18:45:35Z Quantitative Stochastic Homogenization of Elliptic Equations in Nondivergence Form Armstrong, Scott N. Smart, Charles Massachusetts Institute of Technology. Department of Mathematics Smart, Charles We introduce a new method for studying stochastic homogenization of elliptic equations in nondivergence form. The main application is an algebraic error estimate, asserting that deviations from the homogenized limit are at most proportional to a power of the microscopic length scale, assuming a finite range of dependence. The results are new even for linear equations. The arguments rely on a new geometric quantity which is controlled in part by adapting elements of the regularity theory for the Monge–Ampère equation. National Science Foundation (U.S.) (Grant DMS-1004595) 2016-11-04T17:12:22Z 2016-11-04T17:12:22Z 2014-06 2013-12 2016-08-18T15:23:44Z Article http://purl.org/eprint/type/JournalArticle 0003-9527 1432-0673 http://hdl.handle.net/1721.1/105198 Armstrong, Scott N., and Charles K. Smart. “Quantitative Stochastic Homogenization of Elliptic Equations in Nondivergence Form.” Archive for Rational Mechanics and Analysis 214.3 (2014): 867–911. en http://dx.doi.org/10.1007/s00205-014-0765-6 Archive for Rational Mechanics and Analysis Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer-Verlag Berlin Heidelberg application/pdf Springer Berlin Heidelberg Springer Berlin Heidelberg |
| spellingShingle | Armstrong, Scott N. Smart, Charles Quantitative Stochastic Homogenization of Elliptic Equations in Nondivergence Form |
| title | Quantitative Stochastic Homogenization of Elliptic Equations in Nondivergence Form |
| title_full | Quantitative Stochastic Homogenization of Elliptic Equations in Nondivergence Form |
| title_fullStr | Quantitative Stochastic Homogenization of Elliptic Equations in Nondivergence Form |
| title_full_unstemmed | Quantitative Stochastic Homogenization of Elliptic Equations in Nondivergence Form |
| title_short | Quantitative Stochastic Homogenization of Elliptic Equations in Nondivergence Form |
| title_sort | quantitative stochastic homogenization of elliptic equations in nondivergence form |
| url | http://hdl.handle.net/1721.1/105198 |
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