31,219 research outputs found
The fractional p-Laplacian emerging from homogenization of the random conductance model with degenerate ergodic weights and unbounded-range jumps
We study a general class of discrete -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 -Laplace operator.
Under strengthened lower moment conditions, we can apply our insights also to
the spectral homogenization of the discrete Laplace operator to the continuous
fractional Laplace operator
A natural Finsler--Laplace operator
We give a new definition of a Laplace operator for Finsler metric as an
average with regard to an angle measure of the second directional derivatives.
This definition uses a dynamical approach due to Foulon that does not require
the use of connections nor local coordinates. We show using 1-parameter
families of Katok--Ziller metrics that this Finsler--Laplace operator admits
explicit representations and computations of spectral data.Comment: 25 pages, v2: minor modifications, changed the introductio
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