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Issue ESAIM: COCV
Volume 13, Number 2, April-June 2007
Page(s) 294 - 304
DOI 10.1051/cocv:2007018
Published online 12 May 2007

ESAIM: COCV, Vol. 13, N°2, pp. 294-304
DOI: 10.1051/cocv:2007018

Optimal regularity for the pseudo infinity Laplacian

Julio D. Rossi1 and Mariel Saez2

1  Instituto de Matemáticas y Física Fundamental Consejo Superior de Investigaciones Científicas Serrano 123, Madrid, Spain, on leave from Departamento de Matemática, FCEyN UBA (1428) Buenos Aires, Argentina; jrossi@dm.uba.ar
2  Max Planck Institute for Gravitational Physics Albert Einstein Institute Am Mühlenberg 1, 14476 Golm, Germany; mariel.saez@aei.mpg.de


(Received February 27, 2006. Published online 12 May 2007.)

Abstract
In this paper we find the optimal regularity for viscosity solutions of the pseudo infinity Laplacian. We prove that the solutions are locally Lipschitz and show an example that proves that this result is optimal. We also show existence and uniqueness for the Dirichlet problem.


Mathematics Subject Classification. 35A05, 35B65, 35J15

Key words: Viscosity solutions, optimal regularity, pseudo infinity Laplacian


© EDP Sciences, SMAI 2007


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