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pro vyhledávání: '"Kim, Seunghyeok"'
By developing a unified approach based on integral representations, we establish sharp quantitative stability estimates for critical points of the fractional Sobolev inequalities induced by the embedding $\dot{H}^s({\mathbb R}^n) \hookrightarrow L^{2
Externí odkaz:
http://arxiv.org/abs/2408.07775
Autor:
Chen, Haixia, Kim, Seunghyeok
Given a smooth closed Riemannian manifold $(M,g)$ of dimension $N \ge 3$, we derive sharp quantitative stability estimates for nonnegative functions near the solution set of the Yamabe problem on $(M,g)$. The seminal work of Struwe (1984) \cite{S} st
Externí odkaz:
http://arxiv.org/abs/2404.13961
Autor:
Jin, Sangdon, Kim, Seunghyeok
We investigate a novel connection between the weighted isoperimetric problems and the weighted Poisson integrals of the extension problems for nonlocal elliptic operators. We first derive sharp inequalities for the weighted Poisson integrals associat
Externí odkaz:
http://arxiv.org/abs/2310.09160
Autor:
Jin, Sangdon, Kim, Seunghyeok
In this paper, we address the solvability of the critical Lane-Emden system \[\begin{cases} -\Delta u=|v|^{p-1}v &\mbox{in } \Omega_\epsilon,\\ -\Delta v=|u|^{q-1}u &\mbox{in } \Omega_\epsilon,\\ u=v=0 &\mbox{on } \partial \Omega_\epsilon, \end{cases
Externí odkaz:
http://arxiv.org/abs/2210.13068
Autor:
Kim, Seunghyeok, Moon, Sang-Hyuck
We concern a family $\{(u_{\varepsilon},v_{\varepsilon})\}_{\varepsilon > 0}$ of solutions of the Lane-Emden system on a smooth bounded convex domain $\Omega$ in $\mathbb{R}^N$ \[\begin{cases} -\Delta u_{\varepsilon} = v_{\varepsilon}^p &\text{in } \
Externí odkaz:
http://arxiv.org/abs/2202.13599
Autor:
Kim, Seunghyeok, Musso, Monica
Under the validity of the positive mass theorem, the Yamabe flow on a smooth compact Riemannian manifold of dimension $N \ge 3$ is known to exist for all time $t$ and converges to a solution to the Yamabe problem as $t \to \infty$. We prove that if a
Externí odkaz:
http://arxiv.org/abs/2106.09220
Autor:
Kim, Seunghyeok, Pistoia, Angela
We construct families of blowing-up solutions to elliptic systems on smooth bounded domains in the Euclidean space, which are variants of the critical Lane-Emden system and analogous to the Brezis-Nirenberg problem. We find a function which governs b
Externí odkaz:
http://arxiv.org/abs/2004.09191
Autor:
Jin, Sangdon, Kim, Seunghyeok
Publikováno v:
In Journal of Functional Analysis 15 October 2023 285(8)
We prove the non-degeneracy for the critical Lane--Emden system $$ -\Delta U = V^p,\quad -\Delta V = U^q,\quad U, V > 0 \quad \text{in } \mathbb{R}^N $$ for all $N \ge 3$ and $p,q > 0$ such that $\frac{1}{p+1} + \frac{1}{q+1} = \frac{N-2}{N}$. We sho
Externí odkaz:
http://arxiv.org/abs/1908.11122