Duke Mathematical Journal

Subpotential lower bounds for nonnegative solutions to certain quasi-linear degenerate parabolic equations

Emmanuele Dibenedetto, Ugo Gianazza, and Vincenzo Vespri

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Abstract

Nonnegative weak solutions of quasi-linear degenerate parabolic equations of p-Laplacian type are shown to be locally bounded below by Barenblatt-type subpotentials. As a consequence, nonnegative solutions expand their positivity set. That is, a quantitative lower bound on a ball Bρ at time t̲ yields a quantitative lower bound on a ball B2ρ at some further time t. These lower bounds also permit one to recast the Harnack inequality of [4] in a family of alternative, equivalent forms

Article information

Source
Duke Math. J., Volume 143, Number 1 (2008), 1-15.

Dates
First available in Project Euclid: 23 May 2008

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1211574661

Digital Object Identifier
doi:10.1215/00127094-2008-013

Mathematical Reviews number (MathSciNet)
MR2414742

Zentralblatt MATH identifier
1170.35054

Subjects
Primary: 35K65: Degenerate parabolic equations 35B65: Smoothness and regularity of solutions
Secondary: 35B45: A priori estimates

Citation

Dibenedetto, Emmanuele; Gianazza, Ugo; Vespri, Vincenzo. Subpotential lower bounds for nonnegative solutions to certain quasi-linear degenerate parabolic equations. Duke Math. J. 143 (2008), no. 1, 1--15. doi:10.1215/00127094-2008-013. https://projecteuclid.org/euclid.dmj/1211574661


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References

  • E. De Giorgi, Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino. Cl. Sci. Fis. Mat. Nat. (3) 3 (1957), 25--43.
  • E. Dibenedetto, Intrinsic Harnack type inequalities for solutions of certain degenerate parabolic equations, Arch. Rational Mech. Anal. 100 (1988), 129--147.
  • —, Degenerate Parabolic Equations, Universitext, Springer, New York, 1993.
  • E. Dibenedetto, U. Gianazza, and V. Vespri, Harnack estimates for quasi-linear degenerate parabolic differential equations, to appear in Acta Math.
  • E. Dibenedetto and M. A. Herrero, On the Cauchy problem and initial traces for a degenerate parabolic equation, Trans. Amer. Math. Soc. 314, no. 1 (1989), 187--224.
  • J. Moser, A Harnack inequality for parabolic differential equations, Comm. Pure Appl. Math. 17 (1964), 101--134.