Rectifiability of Free Boundaries in Singular Diffusion Problems

Source abstract

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