https://neckpinch.com/authors/jiwoong-jang/New arXiv papers by Jiwoong Jang, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2607.00094arxiv:2607.00094Tue, 30 Jun 2026 00:00:00 GMTTokuhiro Eto, Jiwoong Jang — This paper studies a Chambolle-type minimizing movement scheme for mean curvature flow with prescribed contact angle in a smooth bounded domain. The scheme is based on the capillary functional and the geodesic signed distance relative to the container, and yields a time-discrete level-set approximation. The main result asserts that, for every Lipschitz-continuous boundary function prescribing a strictly nondegenerate contact angle, the approximate solutions converge locally uniformly to the unique viscosity solution of the corresponding level-set mean curvature equation with oblique derivative boundary condition. This improves a previous convergence theorem, where the container was assumed to be convex and a curvature-type condition relating the tangential derivative of the prescribed contact-angle function to the principal curvatures of the container boundary was imposed. The main new ingredient is a uniform Lipschitz estimate for the solutions of the variational problems defining the scheme. This estimate is derived by applying a Bernstein-type argument to a suitable weighted gradient, rather than to the gradient itself, which rules out boundary maxima without relying on the previous curvature-type condition.Mean curvature flowWeak & singular flowsBoundaries & non-compactFree boundary & capillary https://arxiv.org/abs/2509.19470arxiv:2509.19470Tue, 23 Sep 2025 00:00:00 GMTJiwoong Jang — We study the motion of a droplet evolving by mean curvature with volume constraint and contact angle condition on a half space. We prove the existence of a global-in-time weak solution, called the flat flow. A difficulty arises when we establish the local-in-time equi-boundedness of approximate solutions and a uniform L²-estimate of multipliers. The difficulty is handled by conducting blowup analysis at a point in contact to a spherical cap with sharp angle.Mean curvature flowVolume-preserving & constrained flowsSingularitiesWeak & singular flowsFree boundary & capillaryLong-time existence & convergence https://arxiv.org/abs/2503.20014arxiv:2503.20014Tue, 25 Mar 2025 00:00:00 GMTJiwoong Jang, Antoine Mellet — The Patlak-Keller-Segel system of equations (PKS) is a classical example of aggregation-diffusion equation. It describes the aggregation of some organisms via chemotaxis, limited by some nonlinear diffusion. It is known that for some choice of this nonlinear diffusion, the PKS model asymptotically leads to phase separation and mean-curvature driven free boundary problems. In this paper, we focus on the Elliptic-Parabolic PKS model and we obtain the first unconditional convergence result in dimension 2 and 3 towards the volume preserving mean-curvature flow. This work builds up on previous results that were obtained under the assumption that phase separation does not cause energy loss in the limit. In order to avoid this assumption, we rely on Brakke type formulation of the mean-curvature flow and a reinterpretation of the problem as an Allen-Cahn equation with a nonlocal forcing term.Mean curvature flowVolume-preserving & constrained flowsWeak & singular flowsFree boundary & capillaryPhase fields & multiphase flows https://arxiv.org/abs/2501.03455arxiv:2501.03455Tue, 07 Jan 2025 00:00:00 GMTJiwoong Jang — We prove the existence of global-in-time weak solutions to volume-preserving mean curvature flow with in the presence of obstacles by the phase field method in all dimensions. Namely, we prove the convergence of solutions to the Allen-Cahn equation with a multiplier to a weak solution to the flow. The choice of the multiplier is motivated from [Mugnai-Seis-Spadaro '16], [Kim-Kwon '20], and [Takasao '23], which enables us to complete the comparison between the multiplier and the forcing that stops the intrusion into the obstacle. We also prove the vanishing of the discrepancy measure by dealing with the forcing term that is now spatially dependent due to the obstacles.Mean curvature flowVolume-preserving & constrained flowsWeak & singular flowsLong-time existence & convergencePhase fields & multiphase flows https://arxiv.org/abs/2303.17113arxiv:2303.17113Thu, 30 Mar 2023 00:00:00 GMTJiwoong Jang — In this paper, we obtain the rate O(ε^(1/2)) of convergence in periodic homogenization of forced graphical mean curvature flows in the laminated setting. We also discuss with an example that a faster rate cannot be obtained by utilizing Lipscthiz estimates.Mean curvature flowVolume-preserving & constrained flows https://arxiv.org/abs/2112.02715arxiv:2112.02715Mon, 06 Dec 2021 00:00:00 GMTJiwoong Jang — In this paper, we study the forced mean curvature flows and the prescribed mean curvature equations of both graphs and level-sets with capillary-type boundary conditions on a C³ bounded domain, which is not necessarily convex. We prove a priori gradient estimates locally Lipschitz in time. Under an assumption on the forcing term, we prove that the gradient estimates are globally Lipschitz in time. As a consequence, we obtain the existence theorem of solutions. In our formulation, we recover the known results of the gradient estimates on a strictly convex C³ bounded domain. Next, we study the associated eigenvalue problems for mean curvature flows of both graphs and level-sets. We prove the large time behavior of the solutions of mean curvature flows of graphs on a smooth bounded domain. Finally, we compute the asymptotic speed of the solutions of level-set mean curvature flows and the large time profile of level-sets in the radially symmetric case based on optimal control formula. Examples arising in the radially symmetric case demonstrate that the additional assumption on the forcing term is optimal.Mean curvature flowVolume-preserving & constrained flowsBoundaries & non-compactFree boundary & capillaryRotational symmetry & warped productsEigenvalues & spectrum https://arxiv.org/abs/2108.01244arxiv:2108.01244Tue, 03 Aug 2021 00:00:00 GMTJiwoong Jang, Dohyun Kwon, Hiroyoshi Mitake, Hung Vinh Tran — Here, we study a level-set forced mean curvature flow with the homogeneous Neumann boundary condition. We first show that the solution is Lipschitz in time and locally Lipschitz in space. Then, under an additional condition on the forcing term, we prove that the solution is globally Lipschitz. We obtain the large time behavior of the solution in this setting and study the large time profile in some specific situations. Finally, we give two examples demonstrating that the additional condition on the forcing term is sharp, and without it, the solution might not be globally Lipschitz.Mean curvature flowVolume-preserving & constrained flowsHomogeneous spacesBoundaries & non-compactFree boundary & capillary