Author(s):

Fischer, Julian; Raithel, Claudia

Article Title: 
Liouville principles and a largescale regularity theory for random elliptic operators on the halfspace

Affiliation 
IST Austria 
Abstract: 
We consider the largescale regularity of solutions to secondorder 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 halfspace with homogeneous Dirichlet boundary conditions and derive an associated C1,αtype largescale regularity theory in the form of a corresponding decay estimate for the homogenizationadapted tiltexcess. This regularity theory entails an associated Liouvilletype theorem. The results are based on the existence of homogenization correctors adapted to the halfspace setting, which we constructby an entirely deterministic argumentas 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:

10957154

Publisher:

Society for Industrial and Applied Mathematics

Date Published:

20170112

Start Page: 
82

End Page:

114

URL: 

DOI: 
10.1137/16M1070384

Open access: 
yes (repository) 