Differential and Integral Equations

Lower semicontinuity of weak supersolutions to nonlinear parabolic equations

Tuomo Kuusi

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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.

Article information

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

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