A sharp regularity result of solutions of a transmission problem
Authors:
Giovanna Citti and Fausto Ferrari
Journal:
Proc. Amer. Math. Soc. 140 (2012), 615-620
MSC (2010):
Primary 35J20; Secondary 35B65
DOI:
https://doi.org/10.1090/S0002-9939-2011-10916-X
Published electronically:
June 13, 2011
MathSciNet review:
2846330
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: In this paper we study the regularity of solutions of a transmission problem arising in studying a fiber-reinforced composite media. It is described through a divergence type equation div in an open set
, where
is a bounded function and
is a uniformly elliptic matrix, bounded and with piecewise Hölder continuous coefficients. The subdomains
where
is of class
have disjoint closure and are of class
. Exploiting an idea contained in a paper by Li and Vogelius, we obtain the optimal regularity result for solutions, proving that they are of class
.
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Additional Information
Giovanna Citti
Affiliation:
Dipartimento di Matematica, Università Degli Studi di Bologna, Piazza di Porta S. Donato, 5, 40126 Bologna, Italy
Email:
citti@dm.unibo.it
Fausto Ferrari
Affiliation:
Dipartimento di Matematica, Università Degli Studi di Bologna, Piazza di Porta S. Donato, 5, 40126 Bologna, Italy
Email:
ferrari@dm.unibo.it
DOI:
https://doi.org/10.1090/S0002-9939-2011-10916-X
Keywords:
Transmission problems,
sharp regularity
Received by editor(s):
August 2, 2010
Received by editor(s) in revised form:
November 29, 2010
Published electronically:
June 13, 2011
Additional Notes:
The first and second authors were partially supported by M.U.R.S.T., Italy, and CG-DICE project, EU VII Framework Program.
The second author was partially supported by the GNAMPA project “Equazioni non lineari su varietà: proprietà qualitative e classificazione delle soluzioni”.
Communicated by:
Matthew J. Gursky
Article copyright:
© Copyright 2011
American Mathematical Society