Stochastic homogenization of fully nonlinear uniformly elliptic equations revisited
We give a simplified presentation of the obstacle problem approach to stochastic homogenization for elliptic equations in nondivergence form. Our argument also applies to equations which depend on the gradient of the unknown function. In the latter case, we overcome difficulties caused by a lack of...
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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Springer-Verlag
2016
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| Online Access: | http://hdl.handle.net/1721.1/104851 |
| _version_ | 1811087078372409344 |
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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 give a simplified presentation of the obstacle problem approach to stochastic homogenization for elliptic equations in nondivergence form. Our argument also applies to equations which depend on the gradient of the unknown function. In the latter case, we overcome difficulties caused by a lack of estimates for the first derivatives of approximate correctors by modifying the perturbed test function argument to take advantage of the spreading of the contact set. |
| first_indexed | 2024-09-23T13:39:26Z |
| format | Article |
| id | mit-1721.1/104851 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T13:39:26Z |
| publishDate | 2016 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | mit-1721.1/1048512022-10-01T16:22:16Z Stochastic homogenization of fully nonlinear uniformly elliptic equations revisited Armstrong, Scott N Smart, Charles Massachusetts Institute of Technology. Department of Mathematics Smart, Charles We give a simplified presentation of the obstacle problem approach to stochastic homogenization for elliptic equations in nondivergence form. Our argument also applies to equations which depend on the gradient of the unknown function. In the latter case, we overcome difficulties caused by a lack of estimates for the first derivatives of approximate correctors by modifying the perturbed test function argument to take advantage of the spreading of the contact set. National Science Foundation (U.S.) (DMS-1004645) National Sicence Foundation (U.S.) (DMS-1004595) Chaire Junior of la Fondation Sciences Mathématiques de Paris 2016-10-19T17:33:51Z 2016-10-19T17:33:51Z 2013-09 2016-08-18T15:28:27Z Article http://purl.org/eprint/type/JournalArticle 0944-2669 1432-0835 http://hdl.handle.net/1721.1/104851 Armstrong, Scott N., and Charles K. Smart. “Stochastic Homogenization of Fully Nonlinear Uniformly Elliptic Equations Revisited.” Calculus of Variations and Partial Differential Equations, Vol. 50, no. 3–4 (September 2013), pp. 967–980. en http://dx.doi.org/10.1007/s00526-013-0663-z Calculus of Variations and Partial Differential Equations Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ Springer-Verlag Berlin Heidelberg application/pdf Springer-Verlag Springer Berlin Heidelberg |
| spellingShingle | Armstrong, Scott N Smart, Charles Stochastic homogenization of fully nonlinear uniformly elliptic equations revisited |
| title | Stochastic homogenization of fully nonlinear uniformly elliptic equations revisited |
| title_full | Stochastic homogenization of fully nonlinear uniformly elliptic equations revisited |
| title_fullStr | Stochastic homogenization of fully nonlinear uniformly elliptic equations revisited |
| title_full_unstemmed | Stochastic homogenization of fully nonlinear uniformly elliptic equations revisited |
| title_short | Stochastic homogenization of fully nonlinear uniformly elliptic equations revisited |
| title_sort | stochastic homogenization of fully nonlinear uniformly elliptic equations revisited |
| url | http://hdl.handle.net/1721.1/104851 |
| work_keys_str_mv | AT armstrongscottn stochastichomogenizationoffullynonlinearuniformlyellipticequationsrevisited AT smartcharles stochastichomogenizationoffullynonlinearuniformlyellipticequationsrevisited |