Author

Haesung Lee

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Preprint Sep 2026

Notes on linear elliptic equations with $L^2$-gradient perturbations and singular zero-order coefficients

In this paper, we study the existence, uniqueness, and quantitative estimates for weak solutions to linear elliptic Dirichlet problems of the form \[ -\operatorname{div}(\gamma \nabla u)+\langle \nabla\phi+\mathbf{H},\nabla u\rangle+(c+\alpha)u=f \quad\text{ in }U, \quad\; u=0 \quad\text{on }\partial U, \] where $U\sub...

Haesung Lee · 0 citations

Preprint Sep 2026

A weighted semigroup approach to exponential stability in linear parabolic equations

This paper establishes the exponential $L^2$-stability of the unique solutions to initial-boundary value problems for linear parabolic partial differential equations with general drift and zero-order coefficients in bounded domains. The key idea lies in constructing a suitable Dirichlet form with respect to a weighted...

Haesung Lee · 0 citations