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Yong-Cheol Kim

Publications and source records attributed to Yong-Cheol Kim.

At least 19 recordsLinked to original sources
arXiv2026

Large-scale time-series spectroscopy for stellar ages

To date, Galactic Astronomy has largely concerned itself with astrophysical processes, and with the locations, space motions and compositions of objects. Consider, for example, the elucidation of the components of the Galaxy over the past decades, its mapping as enabled by Gaia and its predecessors, the photometric and spectroscopic characterization of innumerable astrophysical objects in various wavelength ranges, both from the ground and from space, and the expanding discovery and characterization of exoplanets; all focused on the current, static Galaxy. This White Paper proposes a dedicated program to derive stellar ages from time-series spectroscopy to hasten the transformation of this static conception into a dynamical one with age-labeled objects and events.

astro-ph.IM↗
arXiv2026

Nonlocal Harnack inequalities for nonlocal double phase equations I ; with positive bounded modulating coefficient with no Hölder condition

In this paper, by applying the De Giorgi-Nash-Moser theory we prove nonlocal Harnack inequalities for (locally nonnegative in $Ω$) weak solutions to nolocal double phase equations \begin{equation*}\begin{cases}\cL u =0 & \text{ in $Ω$,} \\ u=g & \text{ in $\BR^n\sΩ$ } \end{cases}\end{equation*} where $Ω\subset\BR^n$ ($n\ge 2$) is a bounded domain with Lipschitz boundary, $\cL$ is the nonlocal double phase operator $\cL$ given by \begin{equation*}\begin{split}\cL u(x)=&\pv\int_{\BR^n}|u(x)-u(y)|^{p-2}(u(x)-u(y))K_{ps}(x,y)\,dy \\ &+\pv\int_{\BR^n}\fa(x,y)|u(x)-u(y)|^{q-2}(u(x)-u(y))K_{qt}(x,y)\,dy, \end{split} \end{equation*} $0<\fa(x,y) = \fa(y,x) \le \|\fa\|_{L^\iy(\BR^n\times\BR^n)} < \iy$ and $ps\ge qt$ for $0<s,t<1<p\le q<\iy$. In addition, we get local boundedness with explicit formula and weak Harnack inequalities for their weak supersolutions.

math.AP↗
arXiv2023

Hölder regularity of weak solutions to nonlocal $p$-Laplacian type Schrödinger equations with $A_1^p$-Muckenhoupt potentials

In this paper, using the De Giorgi-Nash-Moser method, we obtain an interior Hölder continuity of weak solutions to nonlocal $p$-Laplacian type Schrödinger equations given by an integro-differential operator ${\rm L}^p_K$ ($p>1$) as follows; $$\begin{cases} {\rm L}^p_K u+V|u|^{p-2} u=0 &\text{ in $Ω$, } u=g &\text{ in ${\Bbb R}^n\setminusΩ$ } \end{cases}$$ where $V=V_+-V_-$ with $(V_-,V_+)\in L^1_{loc}({\Bbb R}^n)\times L^q_{loc}({\Bbb R}^n)$ for $q>\frac{n}{ps}>1$ and $0 \frac{n}{ps}>1, 0<s<1$).

math.CA↗
arXiv2018

Nonlocal Harnack inequalities for nonlocal heat equations

In this paper, applying the De Giorgi method, we obtain nonlocal Harnack inequalities for weak solutions of nonlocal parabolic equations given by an integro-differential operator $\rL_K$ as follows; \begin{equation*}\begin{cases} \rL_K u+\pa_t u=0 &\text{ in $\Om\times(-T,0]$ } u=g &\text{ in $\bigl((\BR^n\s\Om)\times (-T,0]\bigr)\cup\bigl(\Om\times\{t=-T\}\bigr)$ } \end{cases}\end{equation*} where $g\in C(\BR^n\times [-T,0])\cap L^{\iy}(\BR^n\times(-T,0])$ and $\,\Om\,$ is a bounded domain in $\BR^n$ with Lipschitz boundary. Moreover, we get nonlocal parabolic weak Harnack inequalities of the weak solutions.

math.AP↗
arXiv2016

The Malgrange-Ehrenpreis theorem for nonlocal Schrödinger operators with certain potentials

In this paper, we prove the Malgrange-Ehrenpreis theorem for nonlocal Schrödinger operators $L_K+V$ with nonnegative potentials $V\in L^q_{\loc}(\BR^n)$ for $q>\f{n}{2s}$ with $0<s<1$ and $n\ge 2$; that is to say, we obtain the existence of a fundamental solution $\fe_V$ for $L_K+V$ satisfying \begin{equation*}\bigl(L_K+V\bigr)\fe_V=\dt_0\,\,\text{ in $\BR^n$ }\end{equation*} in the distribution sense, where $\dt_0$ denotes the Dirac delta mass at the origin. In addition, we obtain a decay of the fundamental solution $\fe_V$.

math.CA↗
arXiv2016

$L^p$ mapping properties for nonlocal Schrödinger operators with certain potential

In this paper, we consider nonlocal Schrödinger equations with certain potentials $V$ given by an integro-differential operator $L_K$ as follows; \begin{equation*}L_K u+V u=f\,\,\text{ in $\BR^n$ }\end{equation*} where $V\in\rh^q$ for $q>\f{n}{2s}$ and $0<s<1$. We denote the solution of the above equation by $\cS_V f:=u$, which is called {\it the inverse of the nonlocal Schrödinger operator $L_K+V$ with potential $V$}; that is, $\cS_V=(L_K+V)^{-1}$. Then we obtain a weak Harnack inequality of weak subsolutions of the nonlocal equation \begin{equation}\begin{cases}L_K u+V u=0\,\,&\text{ in $\Om$,} \quad u=g\,\,&\text{ in $\BR^n\s\Om$,} \end{cases}\end{equation} where $g\in H^s(\BR^n)$ and $\Om$ is a bounded open domain in $\BR^n$ with Lipschitz boundary, and also get an improved decay of a fundamental solution $\fe_V$ for $L_K+V$. Moreover, we obtain $L^p$ and $L^p-L^q$ mapping properties of the inverse $\cS_V$ of the nonlocal Schrödinger operator $L_K+V$.

math.CA↗
arXiv2015

UBVRIz Light Curves of 51 Type II Supernovae

We present a compilation of UBV RIz light curves of 51 type II supernovae discovered during the course of four different surveys during 1986 to 2003: the Cerro Tololo Supernova Survey, the Calan/Tololo Supernova Program (C&T), the Supernova Optical and Infrared Survey (SOIRS), and the Carnegie Type II Supernova Survey (CATS). The photometry is based on template-subtracted images to eliminate any potential host galaxy light contamination, and calibrated from foreground stars. This work presents these photometric data, studies the color evolution using different bands, and explores the relation between the magnitude at maximum brightness and the brightness decline parameter (s) from maximum light through the end of the recombination phase. This parameter is found to be shallower for redder bands and appears to have the best correlation in the B band. In addition, it also correlates with the plateau duration, being thus shorter (longer) for larger (smaller) s values.

astro-ph.SR↗
arXiv2014

Regularity for fully nonlinear integro-differential operators with regularly varying kernels

In this paper, the regularity results for the integro-differential operators of the fractional Laplacian type by Caffarelli and Silvestre \cite{CS1} are extended to those for the integro-differential operators associated with symmetric, regularly varying kernels at zero. In particular, we obtain the uniform Harnack inequality and Hölder estimate of viscosity solutions to the nonlinear integro-differential equations associated with the kernels $K_{σ, β}$ satisfying $$ K_{σ,β}(y)\asymp \frac{ 2-σ}{|y|^{n+σ}}\left( \log\frac{2}{|y|^2}\right)^{β(2-σ)}\quad \mbox{near zero} $$ with respect to $σ\in(0,2)$ close to $2$ (for a given $β\in\mathbb R$), where the regularity estimates do not blow up as the order $ σ\in(0,2)$ tends to $2.$

math.AP↗
arXiv2014

A refinement of the Berezin-Li-Yau type inequality for nonlocal elliptic operators

In this paper, we prove a refinement of the Berezin-Li-Yau type inequality for a wider class of nonlocal elliptic operators including the fractional Laplacians $-(-Δ^{\sm/2})$ restricted to a bounded domain $D\subset\BR^n$ for $n\ge 2$ and $\sm\in (0,2]$, which is optimal when $σ=2$ in view of Weyl's asymptotic formula. In addition, we describe the Berezin-Li-Yau inequality for the Laplacian $Δ$ as the limit case of our result as $\sm\to 2^-$.

math.CA↗
arXiv2012

A proof of the Bochner-Riesz conjecture

For $f\in {\frak S}({\Bbb R}^d)$, we consider the Bochner-Riesz operator ${\frak R}^δ$ of index $δ>0$ defined by $$\hat {{\frak R}^δf}(ξ)=(1-|ξ|^2)^δ_+ \hat f (ξ).$$ Then we prove the Bochner-Riesz conjecture which states that if $δ>\max\{d|1/p-1/2|-1/2,0\}$ and $p>1$ then ${\frak R}^δ$ is a bounded operator from $L^p({\Bbb R}^d)$ into $L^p({\Bbb R}^d)$; moreover, if $δ(p)=d(1/p-1/2)-1/2$ and $1<p<2d/(d+1)$, then ${\frak R}^{δ(p)}$ is a bounded operator from $L^p({\Bbb R}^d)$ into $L^{p,\infty}({\Bbb R}^d)$.

math.CA↗
arXiv2011

Regularity results for fully nonlinear parabolic integro-differential operators

In this paper, we consider the regularity theory for fully nonlinear parabolic integro-differential equations with symmetric kernels. We are able to find parabolic versions of Alexandrov-Backelman-Pucci estimate with 0<σ<2. And we show a Harnack inequality, Hölder regularity, and C^{1,α}-regularity of the solutions by obtaining decay estimates of their level sets.

math.AP↗
arXiv2011

$ζ(5)$ is irrational

We present an elementary proof of the irrationality of $ζ(5)$ based upon the Dirichlet's approximation theorem and the Prime Number Theorem.

math.CA↗
arXiv2011

Regularity results for fully nonlinear integro-differential operators with nonsymmetric positive kernels

In this paper, we consider fully nonlinear integro-differential equations with possibly nonsymmetric kernels. We are able to find different versions of Alexandroff-Backelman-Pucci estimate corresponding to the full class $\cS^{\fL_0}$ of uniformly elliptic nonlinear equations with $1<σ<2$ (subcritical case) and to their subclass $\cS^{\fL_0}_η$ with $0<σ\leq 1$. We show that $\cS^{\fL_0}_η$ still includes a large number of nonlinear operators as well as linear operators. And we show a Harnack inequality, Hölder regularity, and $C^{1,α}$-regularity of the solutions by obtaining decay estimates of their level sets in each cases.

math.AP↗
arXiv2011

Angular Momentum Loss from Cool Stars: An Empirical Expression and Connection to Stellar Activity

We show here that the rotation period data in open clusters allow the empirical determination of an expression for the rate of loss of angular momentum from cool stars on the main sequence. One significant component of the expression, the dependence on rotation rate, persists from prior work; others do not. The expression has a bifurcation, as before, that corresponds to an observed bifurcation in the rotation periods of coeval open cluster stars. The dual dependencies of this loss rate on stellar mass are captured by two functions, $f(B-V)$ and $T(B-V)$, that can be determined from the rotation period observations. Equivalent masses and other [UBVRIJHK] colors are provided in Table 1. Dimensional considerations, and a comparison with appropriate calculated quantities suggest interpretations for $f$ and $T$, both of which appear to be related closely (but differently) to the calculated convective turnover timescale, $τ_c$, in cool stars. This identification enables us to write down symmetrical expressions for the angular momentum loss rate and the deceleration of cool stars, and also to revive the convective turnover timescale as a vital connection between stellar rotation and stellar activity physics.

astro-ph.SR↗
arXiv2010

Regularity results for fully nonlinear integro-differential operators with nonsymmetric positive kernels : Subcritical Case

We introduce a new class of fully nonlinear integro-differential operators with possible nonsymmetric kernels, which includes the ones that arise from stochastic control problems with purely jump Lèvy processes. If the index of the operator $σ$ is in $ (1,2)$ (subcritical case), then we obtain a comparison principle, a nonlocal version of the Alexandroff-Backelman-Pucci estimate, a Harnack inequality, a Hölder regularity, and an interior $\rm C^{1,α}$-regularity for fully nonlinear integro-differential equations associated with such a class. Moreover, our estimates remain uniform as the index $σ$ of the operator is getting close to two, so that they can be regarded as a natural extension of regularity results for elliptic partial differential equations.

math.CA↗