Year: 2026
Type: article
Abstract: Given [Formula: see text] a smooth compact [Formula: see text]-dimensional Riemannian manifold with boundary [Formula: see text]. Let [Formula: see text] be a defining function of [Formula: see text] and [Formula: see text]. In this paper, we study a weighted Sobolev–Poincaré-type trace inequality corresponding to the embedding of [Formula: see text], where [Formula: see text]. More precisely, under some assumptions on the manifold, we prove that there exists a constant [Formula: see text] such that, for all [Formula: see text], [Formula: see text] where [Formula: see text] is a constant depending only on [Formula: see text] and [Formula: see text]. This inequality is sharp in the sense that [Formula: see text] cannot be replaced by any smaller constant. Unlike the classical Sobolev inequality, [Formula: see text] does not depend on [Formula: see text] and [Formula: see text] only, but depends on the manifold.
Authors: Zhongwei Tang, Ning Zhou
Institutions: Beijing Normal University, Nankai University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1028838811, G4561774169, G7056448682
OpenAlex ID: W7124433257
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