9 citations · 18 across the 17 of their papers we have counts for
4 papers · 1 filter
Convergence of Sobolev gradient trajectories to elastica
Shinya Okabe, Philip Schrader
In this paper we study the -gradient flow for the modified elastic energy defined on closed curves in . We prove the existence of a unique global-in-time sol…
The -elastic flow for planar closed curves with constant parametrization
Shinya Okabe, Glen Wheeler
In this paper, we consider the -gradient flow for the modified -elastic energy defined on planar closed curves. We formulate a notion of weak solution for the flow and prov…
Willmore obstacle problems under Dirichlet boundary conditions
Hans-Christoph Grunau, Shinya Okabe
We consider obstacle problems for the Willmore functional in the class of graphs of functions and surfaces of revolution with Dirichlet boundary conditions. We prove the existence…
Existence of solutions to nonlinear parabolic equations via majorant integral kernel
Kazuhiro Ishige, Tatsuki Kawakami, Shinya Okabe
We establish the existence of solutions to the Cauchy problem for a large class of nonlinear parabolic equations including fractional semilinear parabolic equations, higher-order s…