Soojung Kim

activity

20122021

most citedParabolic Harnack inequality of viscosity solutions on Riemannian manifolds

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

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9 papers · 1 filter

math.AP2018

Vanishing time behavior of solutions to the fast diffusion equation

Kin Ming Hui, Soojung Kim

Let $n \geq 3$ , $0 < m < \frac{n - 2}{n}$ and $T > 0$ . We construct positive solutions to the fast diffusion equation $u_{t} = Δ u^{m}$ in $R^{n} \times (0, T)$ , which vanish at time $T$ . By…

math.AP2016★ 2 cited

Twisted solutions to a simplified Ericksen-Leslie equation

Yuan Chen, Soojung Kim, Yong Yu

In this article we construct global solutions to a simplified Ericksen-Leslie system on $R^{3}$ . The constructed solutions are twisted and periodic along the $x_{3}$ -axis with…

math.AP2015★ 1 cited

Asymptotic large time behavior of singular solutions of the fast diffusion equation

Kin Ming Hui, Soojung Kim

We study the asymptotic large time behavior of singular solutions of the fast diffusion equation $u_{t} = Δ u^{m}$ in $(R^{n} ∖ {0}) \times (0, \infty)$ in the subcritical ca…

math.AP2015

Harnack inequality for degenerate and singular operators of $p$ -Laplacian type on Riemannian manifolds

Soojung Kim

We study viscosity solutions to degenerate and singular elliptic equations of $p$ -Laplacian type on Riemannian manifolds. The Krylov-Safonov type Harnack inequality for the $p$ -Lap…

math.AP2014

Estimates on parabolic equations that hold only where the space-time gradient is large

Soojung Kim

We study the Krylov-Safonov type Hölder estimate and Harnack inequality for viscosity solutions satisfying a uniformly parabolic equation only where the gradient with respect to th…

math.AP2014

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

Soojung Kim, Yong-Cheol Kim, Ki-Ahm Lee

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 i…

math.AP2014

Second derivative estimates for uniformly elliptic operators on Riemannian manifolds

Soojung Kim

In this paper, we obtain a uniform $W^{2, ε}$ -estimate of solutions to the fully nonlinear uniformly elliptic equations on Riemannian manifolds with a lower bound of secti…

math.AP2013★ 3 cited

Parabolic Harnack inequality of viscosity solutions on Riemannian manifolds

Soojung Kim, Ki-Ahm Lee

We consider viscosity solutions to nonlinear uniformly parabolic equations in nondivergence form on a Riemannian manifold $M$ , with the sectional curvature bounded from below by $-…

math.AP2012★ 1 cited

Asymptotic Behavior in Degenerate Parabolic Fully Nonlinear equations and its application to Elliptic Eigenvalue Problems

Soojung Kim, Ki-ahm Lee

We study the asymptotic behavior of the nonlinear parabolic flows $u_{t} = F (D^{2} u^{m})$ when $t\ra \infty$ for $m \geq 1$ , and the geometric properties for solutions of the following e…

Vanishing time behavior of solutions to the fast diffusion equation

Twisted solutions to a simplified Ericksen-Leslie equation

Asymptotic large time behavior of singular solutions of the fast diffusion equation

Harnack inequality for degenerate and singular operators of p-Laplacian type on Riemannian manifolds

Estimates on parabolic equations that hold only where the space-time gradient is large

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

Second derivative estimates for uniformly elliptic operators on Riemannian manifolds

Parabolic Harnack inequality of viscosity solutions on Riemannian manifolds

Asymptotic Behavior in Degenerate Parabolic Fully Nonlinear equations and its application to Elliptic Eigenvalue Problems

Harnack inequality for degenerate and singular operators of $p$ -Laplacian type on Riemannian manifolds