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math.AP2022
Coron's problem for the critical Lane-Emden system
Sangdon Jin, Seunghyeok Kim
In this paper, we address the solvability of the critical Lane-Emden system \[\begin{cases} -Δu=|v|^{p-1}v &\mbox{in } Ω_ε,\\ -Δv=|u|^{q-1}u &\mbox{in } Ω_ε,\\ u=v=0 &\mbox{on } \p…
math.AP2022
On steady states for the Vlasov-Schrödinger-Poisson system
Younghun Hong, Sangdon Jin
The Vlasov-Schrödinger-Poisson system is a kinetic-quantum hybrid model describing quasi-lower dimensional electron gases. For this system, we construct a large class of 2D kinetic…
math.AP2022
On the nonlinear Schrödinger equation with a toroidal trap in the strong confinement regime
Younghun Hong, Sangdon Jin
We consider the 3D cubic nonlinear Schrödinger equation (NLS) with a strong toroidal trap. In the first part, we show that as the confinement is strengthened, a large class of glob…