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March  2005, 4(1): 199-207. doi: 10.3934/cpaa.2005.4.187

Uniqueness and existence of maximal and minimal solutions of fully nonlinear elliptic PDE

Robert Jensen 1, and  Andrzej Świech 2,

1. 

Department of Mathematical Sciences, Loyola University of Chicago, 6325 North Sheridan Road, Chicago, IL 60626, United States
2. 

School of Mathematics, Georgia Institute of Technology, 686 Cherry Street, Atlanta, GA 30332-0160, United States

Received  March 2004 Revised  October 2004 Published  December 2004

Two results are proved in the paper. The first is a uniqueness theorem for viscosity solutions of Dirichlet boundary value problems for Bellman-Isaacs equations with just measurable lower order terms. The second is a proof that there always exist maximal and minimal viscosity solutions of Dirichlet boundary value problems for fully nonlinear, uniformly elliptic PDE that are measurable in the $x$-variable.
Keywords: viscosity solutions., Fully nonlinear elliptic PDE.
Mathematics Subject Classification: 35J60, 35J65, 35J25, 49L2.
Citation: Robert Jensen, Andrzej Świech. Uniqueness and existence of maximal and minimal solutions of fully nonlinear elliptic PDE. Communications on Pure & Applied Analysis, 2005, 4 (1) : 199-207. doi: 10.3934/cpaa.2005.4.187
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