Xiangjin Xu

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20082019

most citedUpper and lower bounds for normal derivatives of spectral clusters of Dirichlet Laplacian

2 citations · 3 across the 4 of their papers we have counts for

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math.AP2010★ 2 cited

Upper and lower bounds for normal derivatives of spectral clusters of Dirichlet Laplacian

Xiangjin Xu

In this paper, we prove the upper and lower bounds for normal derivatives of spectral clusters $u = χ_{λ}^{s} f$ of Dirichlet Laplacian $Δ_{M}$ , $$c_s λ\|u\|_{L^2(M)} \leq \| \partial_νu \…

math.AP2008

Gradient estimates for $u_{t} = Δ F (u)$ on manifolds and some Liouville-type theorems

Xiangjin Xu

In this paper, we first prove a localized Hamilton-type gradient estimate for the positive solutions of Porous Media type equations: $u_{t} = Δ F (u),$ with $F^{'} (u) > 0$ , on a complete…

Upper and lower bounds for normal derivatives of spectral clusters of Dirichlet Laplacian

Gradient estimates for ut​=ΔF(u) on manifolds and some Liouville-type theorems

Gradient estimates for $u_{t} = Δ F (u)$ on manifolds and some Liouville-type theorems