A free boundary problem in accretive growth

Fuente: arXiv
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Main Author: Stefanelli, Ulisse
Format: Preprint
Published: 2026
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_version_ 1866912905729933312
author Stefanelli, Ulisse
author_facet Stefanelli, Ulisse
contents We prove an existence result for a free boundary problem inspired by the modelization of accretive growth. The growth process is formulated through a level-set approach, leading to a boundary-value problem for a Hamilton-Jacobi equation within a prescribed constraining set. Existence, variational representability, and regularity of solutions to the growth subproblem are investigated. The full system arises from coupling the growth dynamics with an elliptic equation for the activation field. Existence of solutions to the fully coupled free boundary problems is obtained via an iterative procedure.
format Preprint
id arxiv_https___arxiv_org_abs_2601_08755
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle A free boundary problem in accretive growth
Stefanelli, Ulisse
Analysis of PDEs
35R35, 35F21, 35F30, 35D40
We prove an existence result for a free boundary problem inspired by the modelization of accretive growth. The growth process is formulated through a level-set approach, leading to a boundary-value problem for a Hamilton-Jacobi equation within a prescribed constraining set. Existence, variational representability, and regularity of solutions to the growth subproblem are investigated. The full system arises from coupling the growth dynamics with an elliptic equation for the activation field. Existence of solutions to the fully coupled free boundary problems is obtained via an iterative procedure.
title A free boundary problem in accretive growth
topic Analysis of PDEs
35R35, 35F21, 35F30, 35D40
url https://arxiv.org/abs/2601.08755