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Rendiconti Lincei - Matematica e Applicazioni


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Volume 18, Issue 4, 2007, pp. 359–364
DOI: 10.4171/RLM/502

Published online: 2007-12-31

Intrinsic Harnack inequalities for quasi-linear singular parabolic partial differential equations

Emmanuele DiBenedetto[1], Ugo Gianazza[2] and Vincenzo Vespri[3]

(1) Vanderbilt University, Nashville, United States
(2) Università di Pavia, Italy
(3) Universita di Firenze, Italy

Intrinsic Harnack estimates for non--negative solutions of singular, quasi--linear, parabolic equations, are established, including the prototype $p$--Laplacean equation (\ref{Eq:1:4}) below. For $p$ in the super--critical range $\frac{2N}{N+1}

Keywords: Singular parabolic equations, intrinsic Harnack estimates

DiBenedetto Emmanuele, Gianazza Ugo, Vespri Vincenzo: Intrinsic Harnack inequalities for quasi-linear singular parabolic partial differential equations. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 18 (2007), 359-364. doi: 10.4171/RLM/502