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