https://neckpinch.com/authors/yoshikazu-giga/New arXiv papers by Yoshikazu Giga, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2402.16180arxiv:2402.16180Sun, 25 Feb 2024 00:00:00 GMTTokuhiro Eto, Yoshikazu Giga — We consider a minimizing movement scheme of Chambolle type for the mean curvature flow equation with prescribed contact angle condition in a smooth bounded domain in ℝ^d (d≥2). We prove that an approximate solution constructed by the proposed scheme converges to the level-set mean curvature flow with prescribed contact angle provided that the domain is convex and that the contact angle is away from zero under some control of derivatives of given prescribed angle. We actually prove that an auxiliary function corresponding to the scheme uniformly converges to a unique viscosity solution to the level-set equation with an oblique derivative boundary condition corresponding to the prescribed boundary condition.Mean curvature flowWeak & singular flowsBoundaries & non-compactFree boundary & capillary https://arxiv.org/abs/2306.14218arxiv:2306.14218Sun, 25 Jun 2023 00:00:00 GMTXingzhi Bian, Yoshikazu Giga, Hiroyoshi Mitake — We propose a level-set method for a mean curvature flow whose boundary is prescribed by interpreting the boundary as an obstacle. Since the corresponding obstacle problem is globally solvable, our method gives a global-in-time level-set mean curvature flow under a prescribed boundary with no restriction of the profile of an initial hypersurface. We show that our solution agrees with a classical mean curvature flow under the Dirichlet condition. We moreover prove that our solution agrees with a level-set flow under the Dirichlet condition constructed by P. Sternberg and W. P. Ziemer (1994), where the initial hypersurface is contained in a strictly mean-convex domain and the prescribed boundary is on the boundary of the domain.Mean curvature flowWeak & singular flowsHomogeneous spacesLong-time existence & convergence