Characterization of anisotropic high order Sobolev spaces
Nguyen Lam, Ali Maalaoui, Andrea Pinamonti
TL;DR
This paper develops new characterizations of high order anisotropic Sobolev spaces, extending existing formulas to anisotropic and higher order contexts, which enhances understanding of their structure and properties.
Contribution
It introduces anisotropic versions of Bourgain-Brezis-Mironescu's and Nguyen's formulas for high order Sobolev spaces, providing novel theoretical tools.
Findings
Established anisotropic Bourgain-Brezis-Mironescu formula
Proved Nguyen's formula in anisotropic high order setting
Enhanced theoretical understanding of anisotropic Sobolev spaces
Abstract
We establish two types of characterizations for high order anisotropic Sobolev spaces. In particular, we prove high order anisotropic versions of Bourgain-Brezis- Mironescu's formula and Nguyen's formula.
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 · Nonlinear Partial Differential Equations · Geometric Analysis and Curvature Flows