Year: 2026
Type: preprint
Abstract: We study critical weighted Sobolev trace inequalities on convex cones endowed with positively homogeneous weights. Using mass transportation, we first establish the continuity of the critical trace embedding under general homogeneity and concavity assumptions on the weight. We then identify a compatibility condition between the weight, the cone, and a distinguished direction that makes the transport argument sharp. In this regime, we determine the optimal constant and prove the existence of extremals. Finally, we obtain a complete classification of all nontrivial extremals modulo translation in the lineality space.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223070278