A higher-order large-scale regularity theory for random elliptic operators

@article{Fischer2015AHL,
  title={A higher-order large-scale regularity theory for random elliptic operators},
  author={Julian Fischer and Felix Otto},
  journal={Communications in Partial Differential Equations},
  year={2015},
  volume={41},
  pages={1108 - 1148}
}
  • J. Fischer, F. Otto
  • Published 2015
  • Mathematics
  • Communications in Partial Differential Equations
ABSTRACT We develop a large-scale regularity theory of higher order for divergence-form elliptic equations with heterogeneous coefficient fields a in the context of stochastic homogenization. The large-scale regularity of a-harmonic functions is encoded by Liouville principles: The space of a-harmonic functions that grow at most like a polynomial of degree k has the same dimension as in the constant-coefficient case. This result can be seen as the qualitative side of a large-scale Ck… Expand
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