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Good and viscosity solutions of fully nonlinear elliptic equations

Author(s): Robert Jensen; Maciej Kocan; Andrzej Swiech
Journal: Proc. Amer. Math. Soc. 130 (2002), 533-542.
MSC (2000): Primary 35J60, 35J65, 35J25, 49L25.
Posted: June 6, 2001
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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 $L^p$-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 $L^p$-viscosity solution. The results also extend some results about ``good" solutions of linear equations.

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Additional Information:

Robert Jensen
Affiliation: Department of Mathematical and Computer Sciences, Loyola University, Chicago, Illinois 60626
Email: rrj@math.luc.edu

Maciej Kocan
Affiliation: Department of Mathemetics, University of Cologne, Cologne 50923, Germany
Address at time of publication: Maple Partners Bankhaus, Feuerbachstr. 26-32, 60325 Frankfurt, Germany

Andrzej Swiech
Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
Email: swiech@math.gatech.edu

DOI: 10.1090/S0002-9939-01-06115-9
PII: S 0002-9939(01)06115-9
Received by editor(s): July 5, 2000
Posted: June 6, 2001
Additional Notes: The first author was supported in part by NSF grants DMS-9532030, DMS-9972043 and DMS-9706760.
The second author was supported by an Alexander von Humboldt Fellowship.
The third author was supported in part by NSF grant DMS-9706760. Part of this work was completed while this author was visiting the University of Cologne, supported by the TMR Network ``Viscosity Solutions and their Applications''.
Communicated by: David S. Tartakoff
Copyright of article: Copyright 2001, American Mathematical Society

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