| Popis: |
In this paper, we study variational solutions to parabolic equations of the type ∂tu−divx(Dξf(Du))+Dug(x,u)=0, where u attains time-independent boundary values u0 on the parabolic boundary and f, g fulfill convexity assumptions. We establish a Haar-Rado type theorem: If the boundary values u0 admit a modulus of continuity ω and the estimate |u(x,t)−u0(γ)|≤ω(|x−γ|) holds, then u admits the same modulus of continuity in the spatial variable. Fonds zur Förderung der Wissenschaftlichen Forschung P 31956 |
