Random Homogenization of Fractional Obstacle Problems
L. A. Caffarelli, A. Mellet
TL;DR
This paper investigates the fractional obstacle problem in perforated domains by characterizing the fractional Laplacian as a Dirichlet to Neumann operator, providing insights into homogenization effects.
Contribution
It introduces a novel approach to analyze fractional obstacle problems using the Dirichlet to Neumann characterization in perforated domains.
Findings
Established a new homogenization framework for fractional obstacle problems.
Derived properties of solutions in perforated domains.
Connected fractional Laplacian characterization to obstacle problem analysis.
Abstract
We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem in perforated domains.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Composite Material Mechanics · Numerical methods in inverse problems