Author

Cong-Ming Li

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Preprint Sep 2026

Asymptotic Expansions of the Fundamental Solution for a Mixed Local-Nonlocal Operator

In this paper, we study the fundamental solution of the mixed local-nonlocal operator $ -\Delta+(-\Delta)^s,$ $ 0<s<1. $ We derive precise asymptotic expansions of the fundamental solution and its gradient, up to the first nontrivial correction term, both near the origin and at infinity. The expansions describe the tra...

Cong-Ming Li, Ling Wang, Jiong-Duo Xie · 0 citations

Preprint Sep 2026

$L^p$ isomorphisms for the fractional Laplacian on $\mathbb{R}^n$ and their application

A classical theory of Amrouche, Girault and Giroire (1994) resolves the Laplace equation on $\mathbb{R}^n$ through an isomorphism between weighted Sobolev spaces. Inspired by their framework, we develop the corresponding $L^p$ theory for the fractional Laplacian: we introduce weighted fractional Sobolev spaces $\Lambda...

Cong-Ming Li, Yu-Gao Ouyang, Zi-Xuan Wang · 0 citations