Regularity of a free boundary in parabolic potential theory

Abstract

We study the regularity of the free boundary in a Stefan-type problem \[ Δ u − ∂ t u = χ Ω in D ⊂ R n × R , u = | ∇ u | = 0 on D ∖ Ω \Delta u - \partial _t u = \chi _\Omega \quad \text {in $D\subset \mathbb {R}^n\times \mathbb {R}$}, \qquad u = |\nabla u| = 0 \quad \text {on $D\setminus \Omega $} \] with no sign assumptions on u u and the time derivative ∂ t u \partial _t u .