Jian Wang

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20122024

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math.AP2024

Sharp two-sided heat kernel estimates for Schrödinger operators with decaying potentials

Xin Chen, Jian Wang

We establish global two-sided heat kernel estimates (for full time and space) of the Schrödinger operator $- \frac{1}{2} Δ + V$ on $R^{d}$ , where the potential $V (x)$ is locally bounded…

math.AP2023

Transport of nonlinear oscillations along rays that graze a convex obstacle to any order

Jian Wang, Mark Williams

We provide a geometric optics description in spaces of low regularity, $L^{2}$ and $H^{1}$ , of the transport of oscillations in solutions to linear and some semilinear second-order hyp…