Haesung Lee

collaborators

4 papers

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…

math.PR2025

Cholesky decomposition and well-posedness of Cauchy problem for Fokker-Planck equations with unbounded coefficients

Haesung Lee

This paper explores the well-posedness of the Cauchy problem for the Fokker-Planck equation associated with the partial differential operator $L$ with low regularity condition. To…

math.AP2025

Local elliptic regularity for solutions to stationary Fokker-Planck equations via Dirichlet forms and resolvents

Haesung Lee

In this paper, we show that, for a solution to the stationary Fokker-Planck equation with general coefficients, defined as a measure with an $L^{2}$ -density, this density not only ex…

math.AP2025

Analysis of linear elliptic equations with general drifts and $L^{1}$ -zero-order terms

Haesung Lee

This paper provides a detailed analysis of the Dirichlet boundary value problem for linear elliptic equations in divergence form with $L^{p}$ -general drifts, where $p \in (d, \infty)…

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

Cholesky decomposition and well-posedness of Cauchy problem for Fokker-Planck equations with unbounded coefficients

Local elliptic regularity for solutions to stationary Fokker-Planck equations via Dirichlet forms and resolvents

Analysis of linear elliptic equations with general drifts and L1-zero-order terms

Analysis of linear elliptic equations with general drifts and $L^{1}$ -zero-order terms