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Harmonic morphisms in nonlinear potential theory*

Published online by Cambridge University Press:  22 January 2016

J. Heinonen ,
T. Kilpeläinen  and
O. Martio
J. Heinonen
Affiliation:
University of Michigan Department of Mathematics, Ann Arbor, MI 48109, U.S.A.
T. Kilpeläinen
Affiliation:
University of Jyväskylä Department of Mathematics, P.O. Box 35, 40351 Jyväskylä, Finland
O. Martio
Affiliation:
University of Michigan Department of Mathematics, Ann Arbor, MI 48109, U.S.A.
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This article concerns the following problem: given a family of partial differential operators with similar structure and given a continuous mapping f from an open set Ω in R n into R n, then when does f pull back the solutions of one equation in the family to solutions of another equation in that family? This problem is typical in the theory of differential equations when one wants to use a coordinate change to study solutions in a different environment.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 125 , March 1992 , pp. 115 - 140
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1992

Footnotes

2

Supported by an NSF grant 89-02749.

1

The authors acknowledge the hospitality of the Mittag-Leffler Institute where part of this research was conducted.

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