The Dirichlet problem for non-divergence parabolic equations with discontinuous in time coefficients in a wedge

Abstract

We consider the Dirichlet problem in a wedge for parabolic equation whose coefficients are measurable function of t. We obtain coercive estimates in weighted $L_{p,q}$-spaces. The concept of "critical exponent" introduced in the paper plays here the crucial role. Various important properties of the critical exponent are proved. We give applications to the Dirichlet problem for linear and quasi-linear non-divergence parabolic equations with discontinuous in time coefficients in cylinders $\Omega\times(0,T)$, where $\Omega$ is a bounded domain with an edge or with a conical point.