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arXiv · 2606.28209

Rectifiability of free boundaries in singular diffusion problems

Rafayel Teymurazyan
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Abstract

For minimizers of a degenerate diffusion functional with a singular reaction term, we prove that the free boundary is $(n-1)$-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.

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Rafayel Teymurazyan. 2026-06-26. Rectifiability of free boundaries in singular diffusion problems. https://arxiv.org/abs/2606.28209

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