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Optimal regularity for the pseudo infinity Laplacian

Published online by Cambridge University Press:  12 May 2007

Julio D. Rossi  and
Mariel Saez
Julio D. Rossi
Affiliation:
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; [email protected]
Mariel Saez
Affiliation:
Max Planck Institute for Gravitational Physics Albert Einstein Institute Am Mühlenberg 1, 14476 Golm, Germany; [email protected]
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Abstract

In this paper we find the optimal regularity for viscositysolutions of the pseudo infinity Laplacian. We prove that thesolutions are locally Lipschitz and show an example that provesthat this result is optimal. We also show existence and uniquenessfor the Dirichlet problem.

Keywords

Viscosity solutionsoptimal regularitypseudo infinity Laplacian
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 13 , Issue 2 , April 2007 , pp. 294 - 304
Copyright
© EDP Sciences, SMAI, 2007

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