Haesung Lee

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20242026

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math.AP2026

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

Haesung Lee

In this paper, we study the existence, uniqueness, and quantitative estimates for weak solutions to linear elliptic Dirichlet problems of the form \[ -\operatorname{div}(γ\nabla u)…

math.AP2026

A weighted semigroup approach to exponential stability in linear parabolic equations

Haesung Lee

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 d…

math.PR2026

Weighted Helmholtz--Hodge decompositions, Lyapunov functions, and invariant measures

Haesung Lee, Gerald Trutnau

We study weighted Helmholtz--Hodge decompositions of drift vector fields associated with second-order diffusion operators on $R^{d}$ , $d \geq 2$ . Given a decomposition of the…

Notes on linear elliptic equations with L2-gradient perturbations and singular zero-order coefficients

A weighted semigroup approach to exponential stability in linear parabolic equations

Weighted Helmholtz--Hodge decompositions, Lyapunov functions, and invariant measures

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