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

Tommaso Leonori; José Miguel Urbano

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

Analysis of PDEs 2010-09-17 v2

Authors: Tommaso Leonori , José Miguel Urbano

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.

Keywords

parabolic infinity laplace equation cauchy problem comparison principle uniqueness viscosity solutions polynomial growth

Cite

@article{arxiv.0809.2523,
  title  = {Growth conditions and uniqueness of the Cauchy problem for the evolutionary infinity Laplacian},
  author = {Tommaso Leonori and José Miguel Urbano},
  journal= {arXiv preprint arXiv:0809.2523},
  year   = {2010}
}

Comments

This paper has been withdrawn by the author due to a gap in the proof of Lemma 2.3.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

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