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.

Appeared in

Download Documents