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Advances in Calculus of Variations

Managing Editor: Duzaar, Frank / Kinnunen, Juha

Editorial Board: Armstrong, Scott N. / Balogh, Zoltán / Cardiliaguet, Pierre / Dacorogna, Bernard / Dal Maso, Gianni / DiBenedetto, Emmanuele / Fonseca, Irene / Gianazza, Ugo / Ishii, Hitoshi / Kristensen, Jan / Manfredi, Juan / Martell, Jose Maria / Mingione, Giuseppe / Nystrom, Kaj / Riviére, Tristan / Schaetzle, Reiner / Shen, Zhongwei / Silvestre, Luis / Tonegawa, Yoshihiro / Touzi, Nizar / Wang, Guofang

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Volume 4, Issue 4


Existence results for quasilinear elliptic and parabolic problems with quadratic gradient terms and sources

Lucio Boccardo / Luigi Orsina / Maria Michaela Porzio
Published Online: 2011-02-10 | DOI: https://doi.org/10.1515/acv.2011.006


In this paper we deal with elliptic and parabolic quasilinear problems with a singular quadratic lower order term depending on the gradient, i.e., with the equations


with Ω a bounded open set of , T > 0, M a bounded measurable uniformly elliptic matrix, B > 0, 0 < θ < 1 and 0 < r < 2 – θ. We will prove existence result for solutions under various assumptions on ƒ and the initial datum u 0

Note that the elliptic equation is strongly related with the Euler–Lagrange equation of some integral functionals.

Keywords.: Quasilinear elliptic equations; quasilinear parabolic equations; singular equations

About the article

Received: 2010-10-08

Revised: 2010-12-14

Published Online: 2011-02-10

Published in Print: 2011-09-01

Citation Information: Advances in Calculus of Variations, Volume 4, Issue 4, Pages 397–419, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv.2011.006.

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