Good and viscosity solutions of fully nonlinear elliptic equations

Authors:
Robert Jensen, Maciej Kocan and Andrzej Swiech

Journal:
Proc. Amer. Math. Soc. **130** (2002), 533-542

MSC (2000):
Primary 35J60, 35J65, 35J25, 49L25.

DOI:
https://doi.org/10.1090/S0002-9939-01-06115-9

Published electronically:
June 6, 2001

MathSciNet review:
1862134

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Abstract | References | Similar Articles | Additional Information

We introduce the notion of a ``good" solution of a fully nonlinear uniformly elliptic equation. It is proven that ``good" solutions are equivalent to -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.

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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:
https://doi.org/10.1090/S0002-9939-01-06115-9

Received by editor(s):
July 5, 2000

Published electronically:
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

Article copyright:
© Copyright 2001
American Mathematical Society