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Sobolev imbedding theorems in borderline cases
Author(s):
Nicola
Fusco;
Pierre
Louis
Lions;
Carlo
Sbordone
Journal:
Proc. Amer. Math. Soc.
124
(1996),
561-565.
MSC (1991):
Primary 46E35
MathSciNet review:
1301025
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Abstract:
An imbedding theorem is given for functions whose gradient belongs to a class slightly larger than , .
References:
- ALT
- A. Alvino, P. L. Lions, and G. Trombetti, On optimization problems with prescribed rearrangements, Nonlinear Anal. TMA 13 (1989), 185--220. MR 90c:90236
- BFS
- H. Brèzis, N. Fusco, and C. Sbordone, Integrability for the Jacobian of orientation preserving mappings, J. Funct. Anal. 115 (1993), 425--431. MR 94j:26024
- CLMS
- R. Coifman, P. L. Lions, Y. Meyer, and S. Semmes, Compensated compactness and Hardy spaces, J. Math. Pures Appl. 72 (1993), 247--286. MR 95d:46033
- G
- J. B. Garnett, Bounded analytic functions, Academic Press, New York, 1981. MR 83g:30037
- GT
- D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, Springer, Berlin and New York, 1977. MR 57:13109
- Gr
- L. Greco, A remark on the equality
, Differential and Integral Equations 6 (1993), 1089--1100. MR 95a:49104 - IS
- T. Iwaniec and C. Sbordone, On the integrability of the Jacobian under minimal hypotheses, Arch. Rational Mech. Anal. 119 (1992), 129--143. MR 93i:49057
- Mo
- J. Moser, A sharp form of an inequality by N. Trudinger, Indiana Univ. Math. J. 20 (1971), 1077--1092. MR 46:662
- Mu
- S. Müller, Higher integrability of determinants and weak convergence in
, J. Reine Angew. Math. 412 (1990), 20--34. MR 92b:49026 - RR
- M. M. Rao and Z. D. Ren, Theory of Orlicz spaces, Marcel Dekker, New York, 1991. MR 92e:46059
- T
- N. S. Trudinger, On imbeddings into Orlicz spaces and some applications, J. Math. Mech. 17 (1967), 473--483. MR 35:7121
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Additional Information:
Nicola
Fusco
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Napoli, via Cintia, 80126 Napoli, Italy
Pierre
Louis
Lions
Affiliation:
CEREMADE, Place du Marèchal de Lattre de Tassigny, 75775 Paris Cedex 16, France
Carlo
Sbordone
Affiliation:
Dipartimento di Matematica e Applicazioni, Università di Napoli, via Cintia, 80126 Napoli, Italy
DOI:
10.1090/S0002-9939-96-03136-X
PII:
S 0002-9939(96)03136-X
Received by editor(s):
July 7, 1993
Received by editor(s) in revised form:
September 12, 1994
Communicated by:
Barbara Lee Keyfitz
Copyright of article:
Copyright
1996,
American Mathematical Society
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