%0 Journal Article %1 Kim2017Higher %A Kim, Sunghan %A Lee, Ki-Ahm %D 2017 %J Archive for Rational Mechanics and Analysis %K 35b27-homogenization-equations-in-media-with-periodic-structure %N 3 %P 1273--1304 %R 10.1007/s00205-015-0921-7 %T Higher Order Convergence Rates in Theory of Homogenization I: Equations of Non-divergence Form %U http://dx.doi.org/10.1007/s00205-015-0921-7 %V 219 %X We establish higher order convergence rates in the theory of periodic homogenization of both linear and fully nonlinear uniformly elliptic equations of non-divergence form. The rates are achieved by involving higher order correctors which fix the errors occurring both in the interior and on the boundary layer of our physical domain. The proof is based on a viscosity method and a new regularity theory which captures the stability of the correctors with respect to the shape of our limit profile.

@article{Kim2017Higher, abstract = {{ We establish higher order convergence rates in the theory of periodic homogenization of both linear and fully nonlinear uniformly elliptic equations of non-divergence form. The rates are achieved by involving higher order correctors which fix the errors occurring both in the interior and on the boundary layer of our physical domain. The proof is based on a viscosity method and a new regularity theory which captures the stability of the correctors with respect to the shape of our limit profile.}}, added-at = {2019-03-01T00:11:50.000+0100}, archiveprefix = {arXiv}, author = {Kim, Sunghan and Lee, Ki-Ahm}, biburl = {https://www.bibsonomy.org/bibtex/2e8e1856971b934e60da11a9ea389ca33/gdmcbain}, citeulike-article-id = {14650033}, citeulike-linkout-0 = {http://arxiv.org/abs/1410.6323}, citeulike-linkout-1 = {http://arxiv.org/pdf/1410.6323}, citeulike-linkout-2 = {http://dx.doi.org/10.1007/s00205-015-0921-7}, comment = {Speaking at Recent trends in nonlinear pdes Sydney 2018-11-02}, day = 12, doi = {10.1007/s00205-015-0921-7}, eprint = {1410.6323}, interhash = {fc13bb7a43392bb437fbf916a7cf354c}, intrahash = {e8e1856971b934e60da11a9ea389ca33}, issn = {0003-9527}, journal = {Archive for Rational Mechanics and Analysis}, keywords = {35b27-homogenization-equations-in-media-with-periodic-structure}, month = jan, number = 3, pages = {1273--1304}, posted-at = {2018-11-02 02:10:47}, priority = {2}, timestamp = {2019-03-01T00:11:50.000+0100}, title = {{Higher Order Convergence Rates in Theory of Homogenization I: Equations of Non-divergence Form}}, url = {http://dx.doi.org/10.1007/s00205-015-0921-7}, volume = 219, year = 2017 }