Harmonic Analysis on chord arc domains
E. Milakis, J. Pipher, T. Toro

TL;DR
This paper investigates the solvability of the Dirichlet problem for elliptic operators in complex, non-Lipschitz domains, emphasizing the development of tent space theory on such domains.
Contribution
It introduces a novel approach using tent spaces to analyze elliptic operators in rough, chord arc domains, extending classical results beyond Lipschitz boundaries.
Findings
Established solvability conditions for the Dirichlet problem in chord arc domains.
Developed the theory of tent spaces tailored for rough domains.
Showed that small perturbations of elliptic operators preserve solvability.
Abstract
In the present paper we study the solvability of the Dirichlet problem for second order divergence form elliptic operators with bounded measurable coefficients which are small perturbations of given operators in rough domains beyond the Lipschitz category. In our approach, the development of the theory of tent spaces on these domains is essential.
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 Harmonic Analysis Research · Differential Equations and Boundary Problems · Nonlinear Partial Differential Equations
