Obstacle problems for the elastic flow and related topics

2025/12/25 by Kensuke Yoshizawa, Yoshizawa, Kensuke
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · doi:10.48550/arxiv.2512.21802

openalex publication_date 2025/12/25 · openalex created_date 2025/12/30 · openalex updated_date 2026/07/28

Abstract

In this note, we study an obstacle problem for the elastic flow. We prove the local-in-time existence of weak solutions and discuss their relation to classical solutions when additional regularity is obtained. Related results concerning obstacle problems for the bending energy are also collected.

Citations

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Related

• The elastic flow with obstacles: small obstacle results
• On Gradient Flows with Obstacles and Euler's Elastica
• An Obstacle Problem for Elastic Curves: Existence Results
• On obstacle problem for mean curvature flow with driving force
• On obstacle problem for Brakke's mean curvature flow