Rectifiability of free boundaries in singular diffusion problems

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.

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