A Baire's category method for the Dirichlet problem of quasiregular mappings

Author:
Baisheng Yan

Journal:
Trans. Amer. Math. Soc. **355** (2003), 4755-4765

MSC (2000):
Primary 30C65, 35F30, 49J30

DOI:
https://doi.org/10.1090/S0002-9947-03-03101-5

Published electronically:
July 24, 2003

MathSciNet review:
1997582

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Abstract | References | Similar Articles | Additional Information

Abstract: We adopt the idea of Baire's category method as presented in a series of papers by Dacorogna and Marcellini to study the boundary value problem for quasiregular mappings in space. Our main result is to prove that for any and any piece-wise affine map with for almost every there exists a map such that

The theorems of Dacorogna and Marcellini do not directly apply to our result since the involved sets are unbounded. Our proof is elementary and does not require any notion of polyconvexity, quasiconvexity or rank-one convexity in the vectorial calculus of variations, as required in the papers by the quoted authors.

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Additional Information

**Baisheng Yan**

Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824

Email:
yan@math.msu.edu

DOI:
https://doi.org/10.1090/S0002-9947-03-03101-5

Keywords:
Baire's category method,
Dirichlet problem,
quasiregular mappings

Received by editor(s):
January 25, 2001

Published electronically:
July 24, 2003

Article copyright:
© Copyright 2003
American Mathematical Society