Runcao Lyu

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math.AP2025

$C^{\infty}$ Regularity for the free boundary of one-phase Fractional Laplacian problem

Runcao Lyu

We consider a one-phase free boundary problem involving fractional Laplacian $(- Δ)^{s}$ , $0 < s < 1$ . D. De Silva, O. Savin, and Y. Sire proved that the flat boundaries are $C^{1, α}$ . We…

math.AP2022

2D Thin obstacle problem with data at infinity

Runcao Lyu, Zikai Ye

In this paper, we consider the thin obstacle problem in $R^{2}$ with data at infinity. We first prove the existence and uniqueness of it. Then we show that its symmetric sol…

C∞ Regularity for the free boundary of one-phase Fractional Laplacian problem

2D Thin obstacle problem with data at infinity

$C^{\infty}$ Regularity for the free boundary of one-phase Fractional Laplacian problem