Sharp Sobolev inequalities involving boundary terms revisited
Zhongwei Tang, Jingang Xiong, Ning Zhou
TL;DR
This paper revisits sharp Sobolev inequalities with boundary terms on Riemannian manifolds, emphasizing the influence of mean curvature, and provides new insights into their structure and applications.
Contribution
It offers a new perspective on boundary terms in Sobolev inequalities, highlighting the role of mean curvature and extending previous results.
Findings
Clarifies the role of mean curvature in boundary Sobolev inequalities
Provides refined inequalities involving boundary terms
Enhances understanding of geometric influences on functional inequalities
Abstract
We revisit the sharp Sobolev inequalities involving boundary terms on Riemannian manifolds with boundaries proved by \emph{[Y.Y. Li and M. Zhu, Geom. Funct. Anal. \textbf{8} (1998), 59--87.]} and explore the role of the mean curvature.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering · Numerical methods in inverse problems