Carleman estimates for the parabolic transmission problem and Hölder propagation of smallness across an interface

Propagation of smallness and size estimate in the second order elliptic equation with discontinuous complex Lipschitz conductivity

In this paper, we would like to derive three-ball inequalities and propagation of smallness for the complex second order elliptic equation with discontinuous Lipschitz coefficients. As an application of such estimates, we study the size estimate problem by one pair of Cauchy data on the boundary. The main ingredient in the derivation of three-ball inequalities and propagation of smallness is a local Carleman proved in our recent paper [FVW].

Determining the waveguide conductivity in a hyperbolic equation from a single measurement on the lateral boundary

We consider the multidimensional inverse problem of determining the conductivity coefficient of a hyperbolic equation in an infinite cylindrical domain, from a single boundary observation of the solution. We prove H{ö}lder stability with the aid of a Carleman estimate specifically designed for hyperbolic waveguides.

Kiselev与Nazarov主题的变奏：沿非无散度BMO场的非局部输运-扩散的Hölder估计

Variation on a theme by Kiselev and Nazarov: H{ö}lder estimates for non-local transport-diffusion, along a non-divergence-free BMO field

本文利用对偶演化技术，证明了在扩散主导小尺度且散度负部足够小的条件下，带有分数阶扩散算子和一般BMO输运场的输运-扩散方程的一致Hölder正则性估计，放宽了输运场需有界的限制。

Optimal stability for a first order coefficient in a non-self-adjoint wave equation from dirichlet-to-neumann map

This paper is focused on the study of an inverse problem for a non-self-adjoint hyperbolic equation. More precisely, we attempt to stably recover a first order coefficient appearing in a wave equation from the knowledge of Neumann boundary data. We show in dimension n greater than two, a stability estimate of H{ö}lder type for the inverse problem under consideration. The proof involves the reduction to an auxiliary inverse problem for an electromagnetic wave equation and the use of an appropriate Carleman estimate.

具有奇异势的薛定谔方程的二倍不等式与小性传播

Doubling inequalities and propagation of smallness for Schrödinger equations with singular potentials

本文针对具有奇异复势的薛定谔方程，通过建立尺度不变的 Carleman 不等式证明二倍不等式，并结合多尺度论证实现小性传播，进而给出特征函数对数的 BMO 范数上界。

向后Cahn-Hilliard-反应-扩散问题的Carleman估计

Carleman estimates for backward Cahn-Hilliard-reaction-diffusion problems

针对耦合Cahn-Hilliard-反应-扩散系统的向后逆问题，通过建立四阶/二阶抛物系统的Carleman估计，推导出从单一最终时间观测重构过去状态的Hölder稳定性和对数稳定性，并应用于肿瘤生长模型获得早期状态的向后唯一性和定量稳定性。