4 papers · 1 filter
Global existence and convergence of a density heat flow for strictly subcritical Liouville systems
Zetao Cheng, Haoyu Li, Woongbae Park +1
We study a density heat flow associated with normalized Liouville systems on a closed connected Riemannian surface, and we show that this flow leads to the existence of solutions f…
Synchronized Solutions for Liouville Systems with Sign-Changing Coefficients
Woongbae Park, Lei Zhang
We consider singular Liouville systems on closed Riemann surfaces with a common sign-changing coefficient. Direct continuation from a positive coefficient is obstructed by the unav…
Long Time Existence of A Flow of Elliptic Systems
Woongbae Park, Lei Zhang
For elliptic systems defined on Riemann surfaces, Liouville and Toda systems represent two well-known classes exhibiting drastically different solution structures. Over the years,…
Obstacles for Sobolev-homeomorphisms with low rank -- pointwise a.e. vs distributional Jacobians
Woongbae Park, Armin Schikorra
We show that for any and there exist neither -Sobolev nor -Hölder homeomorphisms from the disk into …