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

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

10.20347/WIAS.PREPRINT.2541

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.

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