Scholarlink

<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(C^{1,\alpha }\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>α</mi> </mrow> </msup> </math></EquationSource> </InlineEquation> 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.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A parabolic free transmission problem: flat free boundaries are smooth

  • 期刊论文

  • 发表日期：

    2025年12月6日

查看全文
  • Dennis Kriventsov,
  • María Soria-Carro

摘要

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 \(C^{1,\alpha }\) C 1 , α 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.