The problem on domains
with piecewise smooth boundaries
with applications
Authors:
Joachim Michel and Mei-Chi Shaw
Journal:
Trans. Amer. Math. Soc. 351 (1999), 4365-4380
MSC (1991):
Primary 35N05, 35N10, 32F10
DOI:
https://doi.org/10.1090/S0002-9947-99-02519-2
Published electronically:
July 9, 1999
MathSciNet review:
1675218
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Let be a bounded domain in
such that
has piecewise smooth boudnary. We discuss the solvability of the Cauchy-Riemann equation
where is a smooth
-closed
form with coefficients
up to the bundary of
,
and
. In particular, Equation (0.1) is solvable with
smooth up to the boundary (for appropriate degree
if
satisfies one of the following conditions:
- i)
-
is the transversal intersection of bounded smooth pseudoconvex domains.
- ii)
-
where
is the union of bounded smooth pseudoconvex domains and
is a pseudoconvex convex domain with a piecewise smooth boundary.
- iii)
-
where
is the intersection of bounded smooth pseudoconvex domains and
is a pseudoconvex domain with a piecewise smooth boundary.

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Additional Information
Joachim Michel
Affiliation:
Université du Littoral, Centre Universitaire de la Mi-Voix, F-62228 Calais, France
Email:
michel@lma.univ-littoral.fr
Mei-Chi Shaw
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email:
mei-chi.shaw.l@nd.edu
DOI:
https://doi.org/10.1090/S0002-9947-99-02519-2
Keywords:
Cauchy-Riemann equations,
piecewise smooth boundary,
tangential Cauchy-Riemann equations.
Received by editor(s):
August 11, 1997
Received by editor(s) in revised form:
May 7, 1998
Published electronically:
July 9, 1999
Additional Notes:
Partially supported by NSF grant DMS 98-01091
Article copyright:
© Copyright 1999
American Mathematical Society