Good and viscosity solutions of fully nonlinear elliptic equations
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- by Robert Jensen, Maciej Kocan and Andrzej Święch PDF
- Proc. Amer. Math. Soc. 130 (2002), 533-542 Request permission
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.References
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Additional Information
- Robert Jensen
- Affiliation: Department of Mathematical and Computer Sciences, Loyola University, Chicago, Illinois 60626
- MR Author ID: 205502
- 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 Święch
- Affiliation: School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332
- Email: swiech@math.gatech.edu
- 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
- © Copyright 2001 American Mathematical Society
- 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
- MathSciNet review: 1862134