Einige Bemerkungen zur Anfangs-Randwertaufgabe $\frac{\partial }{\partial t}u-h(x,t)\Delta u=f$ mit meßbarem Koeffizienten

Abstract

In the present paper the mixed problem $\frac{\partial }{\partial t}u-h(x,t)\Delta u=f$ with measurable coefficient is considered at first for special domains (cubes) by a modification of Banach’s fixed point theorem. Starting from this we get an existence and uniqueness theorem for domains of the class $O^2$. Several properties of the solution are discussed.