website picture
Drawn by @cute_bae_am

Contact

Department of Mathematics,
Republic of Korea Air Force Academy,
Postbox 335-2, 635, Danjae-ro,
Sangdang-gu, Cheongju-si Chungcheongbuk-do,
Republic of Korea

Email. willkwon[at]sogang[dot]ac[dot]kr
Phone. +82-43-290-6593

About me

I’m Hyunwoo Kwon(a.k.a. Will Kwon). I am a full-time lecturer in the Department of Mathematics at Republic of Korea Air Force Academy. Previously, I did my master in mathematics at Sogang University. My advisor was Prof. Hyunseok Kim.

Here is my personal mathematics blog site.

Here is my CV.

The drawing was given by one of my students at Republic of Korea Air Force Academy @cute_bae_am.

Research Interests

My research interests lie on analysis and PDEs. More precisely, I am working and interested on the following topics:

  • dynamics of solutions of equations arisen from physics
  • real-variable methods in harmonic analysis

Publications / Preprints

1. Elliptic equations with drifts in $L^2$ on Lipschitz domains in $\mathbb{R}^2$, arXiv:2104.01300 [math.AP]

Abstract. We consider the Dirichlet problems for second-order elliptic equations with singular drifts given by b. When the leading coefficients $A$ have small mean oscillations in small balls and $\mathrm{div}\,A$, $\mathbf{b}$ are in $L^2$, we obtain $W^{1,p}$-results on bounded Lipschitz domains in $\mathbb{R}^2$ with small Lipschitz constants.

2. Existence and uniqueness of weak solution in $W^{1,2+\varepsilon}$ for elliptic equations with drifts in weak-$L^{n}$ spaces, J. Math. Anal. Appl. 500(1) (2021) 125165, [Journal], arXiv:2011.07524 [math.AP]

Abstract. We consider the following Dirichlet problems for elliptic equations with singular drift $\mathbf{b}$:

$\text{(a)}\, −\mathrm{div}(A\nabla u)+\mathrm{div}(u\mathbf{b})=f,\qquad\text{(b)}\, −\mathrm{div}(A^T\nabla v)−\mathbf{b}\cdot\nabla v=g\quad \text{in } \Omega,$

where $\Omega$ is a bounded Lipschitz domain in $\mathbb{R}^n$, $n\geq 2$. Assuming that $\mathbf{b}\in L^{n,\infty}(\Omega)^n$ has non-negative weak divergence in $\Omega$, we establish existence and uniqueness of weak solution in $W^{1,2+\varepsilon}_0(\Omega)$ of the problem (b) when $A$ is bounded and uniformly elliptic. As an application, we prove unique solvability of weak solution $u$ in $W^{1,2-}_0(\Omega)$ for the problem (a) for every $f\in W^{-1,2-}(\Omega)$.

3. Dirichlet and Neumann problems for elliptic equations with singular drifts on Lipschitz domain, with H. Kim, arXiv:1811.12619 [math.AP]

Abstract. We consider the Dirichlet and Neumann problems for second-order linear elliptic equations:

$−\triangle u+\mathrm{div}(u\mathbf{b})=f\quad \text{and}\quad −\triangle v−\mathbf{b}\cdot\nabla v=g$

in a bounded Lipschitz domain $\Omega$ in $\mathbb{R}^n$ ($n\geq 3$), where $\mathbf{b}:\Omega\rightarrow \mathbb{R}^n$ is a given vector field. Under the assumption that $\mathbf{b}\in L^n(\Omega)^n$, we first establish existence and uniqueness of solutions in $L^p_{\alpha}(\Omega)$ for the Dirichlet and Neumann problems. Here $L^p_{\alpha}(\Omega)$ denotes the Sobolev space (or Bessel potential space) with the pair $(\alpha,p)$ satisfying certain conditions. These results extend the classical works of Jerison-Kenig (1995, JFA) and Fabes-Mendez-Mitrea (1998, JFA) for the Poisson equation. We also prove existence and uniqueness of solutions of the Dirichlet problem with boundary data in $L^2(\partial\Omega)$.

Miscellaneous