## Advances in Differential Equations

### Hölder continuity of local weak solutions for parabolic equations exhibiting two degeneracies

José Miguel Urbano

#### Abstract

We consider equations of the form $${\partial}_{t} v - \mbox{div} ( \alpha (v) \nabla v) = 0 \ ,$$ where $v \in [0,1]$ and $\alpha (v)$ degenerates for $v=0$ and $v=1$. We show that local weak solutions are locally Hölder continuous provided $\alpha$ behaves like a power near the two degeneracies. We adopt the technique of intrinsic rescaling developed by DiBenedetto.

#### Article information

Source
Adv. Differential Equations, Volume 6, Number 3 (2001), 327-358.

Dates
First available in Project Euclid: 2 January 2013

Permanent link to this document

Mathematical Reviews number (MathSciNet)
MR1799489

Zentralblatt MATH identifier
1031.35037

Subjects
Primary: 35K65: Degenerate parabolic equations
Secondary: 35D10 35Q35: PDEs in connection with fluid mechanics

#### Citation

Urbano, José Miguel. Hölder continuity of local weak solutions for parabolic equations exhibiting two degeneracies. Adv. Differential Equations 6 (2001), no. 3, 327--358. https://projecteuclid.org/euclid.ade/1357141214