Daehan Park

activity

20192025

most citedA Sobolev space theory for the Stochastic Partial Differential Equations with space-time non-local operators

2 citations · 7 across the 9 of their papers we have counts for

collaborators

9 papers

math.AP2025

A regularity theory for evolution equations with space-time anisotropic non-local operators in mixed-norm Sobolev spaces

Jae-Hwan Choi, Jaehoon Kang, Daehan Park +1

In this article, we study the regularity of solutions to inhomogeneous time-fractional evolution equations involving anisotropic non-local operators in mixed-norm Sobolev spaces of…

math.PR2024

Sobolev regularity theory for stochastic reaction-diffusion-advection equations with spatially homogeneous colored noises and infinitesimal generators of subordinate Brownian motions

Jae-Hwan Choi, Beom-Seok Han, Daehan Park

This article investigates the existence, uniqueness, and regularity of solutions to nonlinear stochastic reaction-diffusion-advection equations (SRDAEs) with spatially homogeneous…

math.AP2023

An $L_{q} (L_{p})$ -regularity theory for parabolic equations with integro-differential operators having low intensity kernels

Jaehoon Kang, Daehan Park

In this article, we present the existence, uniqueness, and regularity of solutions to parabolic equations with non-local operators $$ \partial_{t}u(t,x) = \mathcal{L}^{a}u(t,x) + f…

math.AP2023★ 1 cited

A regularity theory for parabolic equations with anisotropic non-local operators in $L_{q} (L_{p})$ spaces

Jae-Hwan Choi, Jaehoon Kang, Daehan Park

In this paper, we present an $L_{q} (L_{p})$ -regularity theory for parabolic equations of the form: $\partial_{t} u (t, x) = L^{a, b} (t) u (t, x) + f (t, x), u (0, x) = 0.$ …

math.AP2021★ 1 cited

An $L_{q} (L_{p})$ -theory for time-fractional diffusion equations with nonlocal operators generated by Lévy processes with low intensity of small jumps

Jaehoon Kang, Daehan Park

We investigate an $L_{q} (L_{p})$ -regularity ( $1 < p, q < \infty$ ) theory for space-time nonlocal equations of the type $\partial_{t}^{α} u = L u + f$ . Here, $\partial_{t}^{α}$ is the…

math.PR2021★ 2 cited

A Sobolev space theory for the Stochastic Partial Differential Equations with space-time non-local operators

Kyeong-Hun Kim, Daehan Park, Junhee Ryu

We deal with the Sobolev space theory for the stochastic partial differential equation (SPDE) driven by Wiener processes $$ \partial_{t}^αu=\left( ϕ(Δ) u +f(u) \right) + \partial_t…

math.AP2021

Weighted maximal $L_{q} (L_{p})$ -regularity theory for time-fractional diffusion-wave equations with variable coefficients

Daehan Park

We present a maximal $L_{q} (L_{p})$ -regularity theory with Muckenhoupt weights for the equation \begin{equation}\label{eqn 01.26.16:00} \partial^α_{t}u(t,x)=a^{ij}(t,x)u_{x^{i}x^{j…

math.AP2020★ 1 cited

An $L_{q} (L_{p})$ -theory for diffusion equations with space-time nonlocal operators

Kyeong-hun Kim, Daehan Park, Junhee Ryu

We present an $L_{q} (L_{p})$ -theory for the equation $\partial_{t}^{α} u = ϕ (Δ) u + f, t > 0, x \in R^{d}; u (0, \cdot) = u_{0} .$ Here $p, q > 1$ , $α \in (0, 1)$ , $\partial…

math.AP2019★ 2 cited

Weighted $L_{q} (L_{p})$ -estimate with Muckenhoupt weights for the diffusion-wave equations with time-fractional derivatives

Beom-Seok Han, Kyeong-Hun Kim, Daehan Park

We present a weighted $L_{q} (L_{p})$ -theory ( $p, q \in (1, \infty)$ ) with Muckenhoupt weights for the equation $\partial_{t}^{α} u (t, x) = Δ u (t, x) + f (t, x), t > 0, x \in R^{d} .$ …

A regularity theory for evolution equations with space-time anisotropic non-local operators in mixed-norm Sobolev spaces

Sobolev regularity theory for stochastic reaction-diffusion-advection equations with spatially homogeneous colored noises and infinitesimal generators of subordinate Brownian motions

An Lq​(Lp​)-regularity theory for parabolic equations with integro-differential operators having low intensity kernels

A regularity theory for parabolic equations with anisotropic non-local operators in Lq​(Lp​) spaces

An Lq​(Lp​)-theory for time-fractional diffusion equations with nonlocal operators generated by Lévy processes with low intensity of small jumps