Existence of  boundary blow up solutions for singular or degenerate  fully nonlinear equations

Françoise Demengel; O. Goubet

doi:10.3934/cpaa.2013.12.621

Article Contents

2013, Volume 12, Issue 2: 621-645. Doi: 10.3934/cpaa.2013.12.621

This issue Previous Article Next Article The decay estimates of solutions for 1D compressible flows with density-dependent viscosity coefficients

Existence of boundary blow up solutions for singular or degenerate fully nonlinear equations

Françoise Demengel^1, and
O. Goubet^2,

1.
AGM UMR 8088, Universié de Cergy Pontoise, UFR Sciences et techniques Site Saint Martin, BP 222 95302, Cergy Pontoise Cedex
2.
LAMFA CNRS UMR 6140, Université de Picardie Jules Verne, 33 rue Saint-Leu 80039 Amiens cedex

Received: June 30, 2011

Revised: January 31, 2012

Published: February 2013

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Abstract

We prove here the existence of boundary blow up solutions for fully nonlinear equations in general domains, for a nonlinearity satisfying Keller-Osserman type condition. If moreover the nonlinearity is non decreasing, we prove uniqueness for boundary blow up solutions on balls for operators related to Pucci's operators.

Keywords:

Boundary blow up solutions,
fully nonlinear equations.

Mathematics Subject Classification: 35J60, 35B44.

Citation:

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