Differential and Integral Equations
- Differential Integral Equations
- Volume 22, Number 11/12 (2009), 1211-1222.
Lower semicontinuity of weak supersolutions to nonlinear parabolic equations
We prove that weak supersolutions to equations similar to the evolutionary $p$-Laplace equation have lower semicontinuous representatives. The proof avoids the use of Harnack's inequality and, in particular, the use of parabolic BMO. Moreover, the result gives a new point of view to approaching the continuity of the solutions to a second-order partial differential equation in divergence form.
Differential Integral Equations, Volume 22, Number 11/12 (2009), 1211-1222.
First available in Project Euclid: 20 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35K92: Quasilinear parabolic equations with p-Laplacian
Secondary: 35B51: Comparison principles
Kuusi, Tuomo. Lower semicontinuity of weak supersolutions to nonlinear parabolic equations. Differential Integral Equations 22 (2009), no. 11/12, 1211--1222. https://projecteuclid.org/euclid.die/1356019413