A Boundary Estimate for Singular Sub-Critical Parabolic Equations

Abstract

We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to singular parabolic equations of $p$-laplacian type, with $p$ in the sub-critical range $(1,\frac{2N}{N+1}]$. The estimate is given in terms of a Wiener-type integral, defined by a proper elliptic $p$-capacity.