Quantitative homogenization for the obstacle problem and its free boundary
Gohar Aleksanyan, Tuomo Kuusi
TL;DR
This paper establishes quantitative homogenization results for the obstacle problem with measurable coefficients, leading to improved large-scale regularity of solutions and free boundaries in heterogeneous environments.
Contribution
It introduces new quantitative homogenization techniques for the obstacle problem with measurable coefficients, enhancing understanding of free boundary regularity in heterogeneous media.
Findings
Quantitative homogenization results for the obstacle problem.
Large-scale regularity of solutions and free boundaries.
Applicability to heterogeneous coefficients.
Abstract
In this manuscript we prove quantitative homogenization results for the obstacle problem with bounded measurable coefficients. As a consequence, large-scale regularity results both for the solution and the free boundary for the heterogeneous obstacle problem are derived.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Geometric and Algebraic Topology · Computational Geometry and Mesh Generation