A parabolic free transmission problem: flat free boundaries are smooth

Autor:	Kriventsov, Dennis, Soria-Carro, María
Rok vydání:	2024
Předmět:	Mathematics - Analysis of PDEs 35B65 35R35 (Primary) 35K05 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We study a two-phase parabolic free boundary problem motivated by the jump of conductivity in composite materials that undergo a phase transition. Each phase is governed by a heat equation with distinct thermal conductivity, and a transmission-type condition is imposed on the free interface. We establish strong regularity properties of the free boundary: first, we prove that flat free boundaries are $C^{1,\alpha}$ by means of a linearization technique and compactness arguments. Then we use the Hodograph transform to achieve higher regularity. To this end, we prove a new Harnack-type inequality and develop the Schauder theory for parabolic linear transmission problems. Comment: 34 pages, 2 figures; slightly improved Section 8
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2402.16805 Zobrazit plný text záznamu View this record from Arxiv