Reveals solutions and growth characteristics of free boundaries in nonlinear equations, indicating optimal solutions exist.
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.
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Byun et al. (2026) studied this question.
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