Author

Jiong-Duo Xie

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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

Mass Bounds for Confined Area-Minimizing Minimal Surfaces

We establish codimension-independent mass bounds for geometrically confined area-minimizing rectifiable currents. In Euclidean space, we combine the confined-volume doubling theorem of Colding--Minicozzi with a current-theoretic squashing argument. This gives an affirmative answer to Lin's interior mass-bound problem f...

Xu-Min Jiang, Jiong-Duo Xie · 0 citations