Growth conditions and uniqueness of the Cauchy problem for the evolutionary infinity Laplacian

Tommaso Leonori; José Miguel Urbano

paper

Growth conditions and uniqueness of the Cauchy problem for the evolutionary infinity Laplacian

arXiv:0809.2523

Abstract

We study the Cauchy problem for the parabolic infinity Laplace equation. We prove a new comparison principle and obtain uniqueness of viscosity solutions in the class of functions with a polinomial growth at infinity, improving previous results obtained assuming a linear growth.

arXiv commentThis paper has been withdrawn by the author due to a gap in the proof of Lemma 2.3. In fact, the condition $Φ (x, y, 0, 0) \leq 0$ does not directly follow from (6) and (7)