### Integrability and boundedness of local solutions to doubly degenerate quasilinear parabolic equations

Mike O'Leary

#### Abstract

Integral and supremum estimates are proven for local solutions of doubly degenerate quasilinear parabolic equations. This is done with the aid of a local energy inequality and estimates in $L^{\text{weak}}_q$ spaces.

#### Article information

Source
Adv. Differential Equations, Volume 5, Number 10-12 (2000), 1465-1492.

Dates
First available in Project Euclid: 27 December 2012

Mathematical Reviews number (MathSciNet)
MR1785682

Zentralblatt MATH identifier
0987.35085

Subjects
Primary: 35K65: Degenerate parabolic equations
Secondary: 35B35: Stability 35K55: Nonlinear parabolic equations

#### Citation

O'Leary, Mike. Integrability and boundedness of local solutions to doubly degenerate quasilinear parabolic equations. Adv. Differential Equations 5 (2000), no. 10-12, 1465--1492. https://projecteuclid.org/euclid.ade/1356651230