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<p>In this paper we prove that solutions to a transmission problem degenerating on the interface are Hölder differentiable up to the interface with universal estimates. Furthermore, we obtain a sharper pointwise <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(C^{1,\alpha (\cdot )}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>α</mi> <mo stretchy="false">(</mo> <mo>·</mo> <mo stretchy="false">)</mo> </mrow> </msup> </math></EquationSource> </InlineEquation> with optimal variable exponent and uniform estimates. Our results also establish a comprehensive theory for degenerate transmission problems with flat interfaces, covering the existence, comparison principle and uniqueness of solutions.</p>

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A fully nonlinear transmission problem degenerating on the interface

  • 期刊论文

  • 发表日期：

    2026年2月17日

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  • Davide Giovagnoli,
  • David Jesus

摘要

In this paper we prove that solutions to a transmission problem degenerating on the interface are Hölder differentiable up to the interface with universal estimates. Furthermore, we obtain a sharper pointwise \(C^{1,\alpha (\cdot )}\) C 1 , α ( · ) with optimal variable exponent and uniform estimates. Our results also establish a comprehensive theory for degenerate transmission problems with flat interfaces, covering the existence, comparison principle and uniqueness of solutions.