# A Non-Degeneracy Property for a Class of Degenerate Parabolic Equations

### Carsten Ebmeyer

Universität Bonn, Germany

## Abstract

We deal with the initial and boundary value problem for the degenerate parabolic equation $u_{t}=Δβ(u)$ in the cylinder $Ω×(0,T)$, where $Ω⊂R_{n}$ is bounded, $β(0)=β’(0)=0$, and $β_{′}≥0$ (e.g., $β(u)=u∣u∣_{m–1}(m>1))$. We study the appearance of the free boundary, and prove under certain hypothesis on $β$ that the free boundary has a finite speed of propagation, and is Holder continuous. Further, we estimate the Lebesgue measure of the set where $u>0$ is small and obtain the non-degeneracy property $∣{0<β_{′}(u(x,t))<ϵ}∣≤cϵ_{21}$.

## Cite this article

Carsten Ebmeyer, A Non-Degeneracy Property for a Class of Degenerate Parabolic Equations. Z. Anal. Anwend. 15 (1996), no. 3, pp. 637–650

DOI 10.4171/ZAA/720