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<p>We study minimizing cones in the Alt-Phillips problem for when the exponent <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation> is for close to 1. For when <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation> converges to 1, we show that the cones concentrate around <i>symmetric</i> solutions to the classical obstacle problem. To be precise, the limiting profiles are radial in a subspace and invariant in directions perpendicular to that subspace.</p>

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Concentration of Cones in the Alt-Phillips Problem

  • 期刊论文

  • 发表日期：

    2026年5月8日

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  • Ovidiu Savin,
  • Hui Yu

摘要

We study minimizing cones in the Alt-Phillips problem for when the exponent \(\gamma \) γ is for close to 1. For when \(\gamma \) γ converges to 1, we show that the cones concentrate around symmetric solutions to the classical obstacle problem. To be precise, the limiting profiles are radial in a subspace and invariant in directions perpendicular to that subspace.