Zobrazeno 1 - 10
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pro vyhledávání: '"Choi, Jae Hwan"'
Autor:
Choi, Jae-Hwan, Kim, Ildoo
In this paper, we aim to develop a new weak formulation that ensures well-posedness for a broad range of stochastic partial differential equations with pseudo-differential operators whose symbols depend only on time and spatial frequencies. The main
Externí odkaz:
http://arxiv.org/abs/2408.04529
This article investigates the existence, uniqueness, and regularity of solutions to nonlinear stochastic reaction-diffusion-advection equations (SRDAEs) with spatially homogeneous colored noises and variable-order nonlocal operators in mixed norm $L_
Externí odkaz:
http://arxiv.org/abs/2405.11969
Autor:
Choi, Jae-Hwan, Kim, Ildoo
We broaden the domain of the Fourier transform to contain all distributions without using the Paley-Wiener theorem and devise a new weak formulation built upon this extension. This formulation is applicable to evolution equations involving pseudo-dif
Externí odkaz:
http://arxiv.org/abs/2403.19968
Autor:
Choi, Jae-Hwan
This paper investigates the existence, uniqueness, and regularity of solutions to evolution equations with time-measurable pseudo-differential operators in weighted mixed-norm Sobolev-Lipschitz spaces. We also explore trace embedding and continuity o
Externí odkaz:
http://arxiv.org/abs/2402.03609
In this paper, we study different types of weighted Besov and Triebel-Lizorkin spaces with variable smoothness. The function spaces can be defined by means of the Littlewood-Paley theory in the field of Fourier analysis, while there are other norms a
Externí odkaz:
http://arxiv.org/abs/2309.01359
This paper considers traces at the initial time for solutions of evolution equations with local or non-local derivatives in vector-valued $L_p$ spaces with $A_p$ weight. To achieve this, we begin by introducing a generalized real interpolation method
Externí odkaz:
http://arxiv.org/abs/2309.00370
In this paper, we present an $L_q(L_p)$-regularity theory for parabolic equations of the form: $$ \partial_t u(t,x)=\mathcal{L}^{\vec{a},\vec{b}}(t)u(t,x)+f(t,x),\quad u(0,x)=0. $$ Here, $\mathcal{L}^{\vec{a},\vec{b}}(t)$ represents anisotropic non-l
Externí odkaz:
http://arxiv.org/abs/2308.00347
In this study, we investigate the existence, uniqueness, and maximal regularity estimates of solutions to homogeneous initial value problems involving time-measurable pseudo-differential operators within the framework of weighted mixed norm Lebesgue
Externí odkaz:
http://arxiv.org/abs/2302.07507
Autor:
Choi, Jae-Hwan, Kim, Ildoo
We obtain the existence, uniqueness, and regularity estimates of the following Cauchy problem \begin{equation}\label{ab eqn} \begin{cases} \partial_t u(t,x)=\psi(t,-i\nabla)u(t,x)+f(t,x),\quad &(t,x)\in(0,T)\times\mathbb{R}^d,\\ u(0,x)=0,\quad & x\in
Externí odkaz:
http://arxiv.org/abs/2205.12463
We study the zero exterior problem for the elliptic equation $$ \Delta^{\alpha/2}u-\lambda u=f, \quad x\in D\,; \quad u|_{D^c}=0 $$ as well as for the parabolic equation $$ u_t=\Delta^{\alpha/2}u+f, \quad t>0,\, x\in D \,; \quad u(0,\cdot)|_D=u_0, \,
Externí odkaz:
http://arxiv.org/abs/2205.11035