Liouville principles and a large-scale regularity theory for random elliptic operators on the half-space Journal Article


Author(s): Fischer, Julian; Raithel, Claudia
Article Title: Liouville principles and a large-scale regularity theory for random elliptic operators on the half-space
Affiliation
Abstract: We consider the large-scale regularity of solutions to second-order linear elliptic equations with random coefficient fields. In contrast to previous works on regularity theory for random elliptic operators, our interest is in the regularity at the boundary: We consider problems posed on the half-space with homogeneous Dirichlet boundary conditions and derive an associated C1,α-type large-scale regularity theory in the form of a corresponding decay estimate for the homogenization-adapted tilt-excess. This regularity theory entails an associated Liouville-type theorem. The results are based on the existence of homogenization correctors adapted to the half-space setting, which we construct-by an entirely deterministic argument-as a modification of the homogenization corrector on the whole space. This adaption procedure is carried out inductively on larger scales, crucially relying on the regularity theory already established on smaller scales.
Keywords: random elliptic operator; stochastic homogenization; Boundary regularity
Journal Title: SIAM Journal on Mathematical Analysis
Volume: 49
Issue 1
ISSN: 1095-7154
Publisher: Society for Industrial and Applied Mathematics  
Date Published: 2017-01-12
Start Page: 82
End Page: 114
URL:
DOI: 10.1137/16M1070384
Open access: yes (repository)
IST Austria Authors
  1. Julian Fischer
    15 Fischer