American Institute of Mathematical Sciences

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

 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.
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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