논문KCI 등재
The Michael-Simon-Sobolev inequality for positive symmetric tensor fields
대한수학회 (The Korean Mathematical Society)|2025.07|대한수학회보 (Bulletin of the KMS)|제62권 제4호|pp. 1059-1071|DOI 10.4134/BKMS.b240368
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Inspired by \cite{Bre, DP}, we prove the Michael-Simon type Sobolev inequality for smooth symmetric uniformly positive definite $\left( 0,2\right)$-tensor fields on a compact submanifold in Euclidean space by the Alexandrov-Bakelman-Pucci (ABP) method. It is a slight generalization of S. Brendle in \cite{Bre}.
Abstract
Inspired by \cite{Bre, DP}, we prove the Michael-Simon type Sobolev inequality for smooth symmetric uniformly positive definite $\left( 0,2\right)$-tensor fields on a compact submanifold in Euclidean space by the Alexandrov-Bakelman-Pucci (ABP) method. It is a slight generalization of S. Brendle in \cite{Bre}.
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