WIAS Preprint No. 2541, (2018)
The fractional p-Laplacian emerging from homogenization of the random conductance model with degenerate ergodic weights and unbounded-range jumps
Authors
- Flegel, Franziska
- Heida, Martin
ORCID: 0000-0002-7242-8175
2010 Mathematics Subject Classification
- 80M40 60H25 60K37 35B27 35R60 47B80 47A75
Keywords
- Random conductance, degenerate weights, fractional Laplace operator, p-Laplace, fractional p-Laplacian, stochastic homogenization, random walk
DOI
Abstract
We study a general class of discrete p-Laplace operators in the random conductance model with long-range jumps and ergodic weights. Using a variational formulation of the problem, we show that under the assumption of bounded first moments and a suitable lower moment condition on the weights, the homogenized limit operator is a fractional p-Laplace operator. Under strengthened lower moment conditions, we can apply our insights also to the spectral homogenization of the discrete Lapalace operator to the continuous fractional Laplace operator.
Appeared in
- Calc. Var. Partial Differ. Equ., Published online on 28.11.2019, DOI 10.1007/s00526-019-1663-4 .
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