Authors: Schweizer, Ben
Melcher, Christof
Title: Direct approach to L^p estimates in homogenization theory
Language (ISO): en
Abstract: We derive interior L^p-estimates for solutions of linear elliptic systems with oscillatory coefficients. The estimates are independent of e, the small length scale of the rapid oscillations. So far, such results are based on potential theory and restricted to periodic coefficients. Our approach relies on BMO-estimates and an interpolation argument, gradients are treated with the help of finite differences. This allows to treat coefficients that depend on a fast and a slow variable. The estimates imply an L^p-corrector result for approximate solutions.
Subject Headings: heterogeneous media
elliptic systems
regularity theory
BMO
two-scale convergence
URI: http://hdl.handle.net/2003/26958
http://dx.doi.org/10.17877/DE290R-153
Issue Date: 2008-03-26
Rights: © Springer-Verlag 2008
Publisher: Springer-Verlag
URL: http://dx.doi.org/10.1007/s10231-008-0078-1
Citation: Melcher, Christof; Schweizer, Ben: Direct approach to L^p estimates in homogenization theory. - In: Annali di Matematica Pura ed Applicata, 188(3), 399, 2009. - DOI: 10.1007/s10231-008-0078-1
Appears in Collections:Schweizer, Ben Prof. Dr.

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