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<p>For minimizers of a degenerate diffusion functional with a singular reaction term, we prove that the free boundary is <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((n-1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-rectifiable. The argument relies on a suitable integrability property, derived from a pointwise gradient estimate, combined with a Hausdorff dimension estimate for a portion of the zero set.</p>

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Rectifiability of Free Boundaries in Singular Diffusion Problems

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月9日

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  • Rafayel Teymurazyan

摘要

For minimizers of a degenerate diffusion functional with a singular reaction term, we prove that the free boundary is \((n-1)\) ( n - 1 ) -rectifiable. The argument relies on a suitable integrability property, derived from a pointwise gradient estimate, combined with a Hausdorff dimension estimate for a portion of the zero set.