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Good and viscosity solutions of fully nonlinear elliptic equations |
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| Authors: | Robert Jensen Maciej Kocan Andrzej Swiech |
| Institution: | Department of Mathematical and Computer Sciences, Loyola University, Chicago, Illinois 60626 ; Department of Mathemetics, University of Cologne, Cologne 50923, Germany ; School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332 |
| Abstract: | We introduce the notion of a ``good" solution of a fully nonlinear uniformly elliptic equation. It is proven that ``good" solutions are equivalent to |
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-viscosity solutions of such equations. The main contribution of the paper is an explicit construction of elliptic equations with strong solutions that approximate any given fully nonlinear uniformly elliptic equation and its 
-viscosity solution. The results also extend some results about ``good" solutions of linear equations.