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<p>We study fully nonlinear uniformly elliptic equations with logarithmic singular absorption terms. In the absence of scaling properties, we establish the existence of solutions and characterize their optimal growth along the free boundary and sharp local regularity. Additionally, we derive non-degeneracy results and provide finer geometric estimates for the free boundary.</p>

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On fully nonlinear free boundary problem with logarithmic singular absorption terms

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年2月17日

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  • Sun-Sig Byun,
  • SeungHyun Kim

摘要

We study fully nonlinear uniformly elliptic equations with logarithmic singular absorption terms. In the absence of scaling properties, we establish the existence of solutions and characterize their optimal growth along the free boundary and sharp local regularity. Additionally, we derive non-degeneracy results and provide finer geometric estimates for the free boundary.