Free boundary regularity in nonlinear one-phase Stefan problem

2024/04/10 by Yamin Wang, Wang, Yamin
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2404.06712

openalex publication_date 2024/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the regularity of the free boundary in one-phase Stefan problem with nonlinear operator. Using the Hodograph transform and a linearization technique, we prove that flat free boundaries are C^{1, α} in space and time. When the operator is concave (or convex) and smooth, the free boundary is smooth.

Related

• Free boundary regularity for the inhomogeneous one-phase Stefan problem
• Perturbative estimates for the one-phase Stefan Problem
• Existence and regularity in the fully nonlinear one-phase free boundary problem
• On the Geometry of Solutions of the Fully Nonlinear Inhomogeneous One-Phase Stefan Problem
• Free boundary regularity for a problem with right hand side