Rectifiability of free boundaries in singular diffusion problems

Rafayel Teymurazyan

Rectifiability of free boundaries in singular diffusion problems

Analysis of PDEs 2026-06-26 v1

Authors: Rafayel Teymurazyan

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.

Cite

@article{arxiv.2606.28209,
  title  = {Rectifiability of free boundaries in singular diffusion problems},
  author = {Rafayel Teymurazyan},
  journal= {arXiv preprint arXiv:2606.28209},
  year   = {2026}
}

Comments

Bull. Braz. Math. Soc. (N.S.)