Sharp exponential integrability for traces of monotone Sobolev functions
Pekka Pankka, Pietro Poggi-Corradini, and Kai Rajala
Source: Nagoya Math. J. Volume 192 (2008), 137-149.
Abstract
We answer a question posed in [12] on exponential integrability of functions of restricted $n$-energy. We use geometric methods to obtain a sharp exponential integrability result for boundary traces of monotone Sobolev functions defined on the unit ball.
Primary Subjects: 46E35
Secondary Subjects: 31C45
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.nmj/1229955909
Mathematical Reviews number (MathSciNet):
MR2477615
Zentralblatt MATH identifier:
05490763
References
S.-Y. A. Chang and D. E. Marshall, On a sharp inequality concerning the Dirichlet integral, Amer. J. Math., 107(5) (1985), 1015--1033.
Mathematical Reviews (MathSciNet):
MR805803
Digital Object Identifier: doi:10.2307/2374345
JSTOR: links.jstor.org
L. C. Evans and R. F. Gariepy, Measure theory and fine properties of functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992.
Mathematical Reviews (MathSciNet):
MR1158660
B. Fuglede, Extremal length and functional completion, Acta Math., 98 (1957), 171--219.
Mathematical Reviews (MathSciNet):
MR97720
Digital Object Identifier: doi:10.1007/BF02404474
F. W. Gehring, Symmetrization of rings in space, Trans. Amer. Math. Soc., 101 (1961), 499--519.
Mathematical Reviews (MathSciNet):
MR132841
Digital Object Identifier: doi:10.2307/1993475
F. W. Gehring, Rings and quasiconformal mappings in space, Trans. Amer. Math. Soc., 103 (1962), 353--393.
Mathematical Reviews (MathSciNet):
MR139735
Digital Object Identifier: doi:10.2307/1993834
JSTOR: links.jstor.org
J. Heinonen, T. Kilpeläinen, and O. Martio, Nonlinear potential theory of degenerate elliptic equations, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, 1993.
Mathematical Reviews (MathSciNet):
MR1207810
J. Malý, D. Swanson, and W. P. Ziemer, The co-area formula for Sobolev mappings, Trans. Amer. Math. Soc., 355(2) (2003), 477--492 (electronic).
Mathematical Reviews (MathSciNet):
MR1932709
Digital Object Identifier: doi:10.1090/S0002-9947-02-03091-X
J. J. Manfredi, Weakly monotone functions, J. Geom. Anal., 4(3) (1994), 393--402.
Mathematical Reviews (MathSciNet):
MR1294334
D. E. Marshall, A new proof of a sharp inequality concerning the Dirichlet integral, Ark. Mat., 27(1) (1989), 131--137.
Mathematical Reviews (MathSciNet):
MR1004727
J. Moser, A sharp form of an inequality by N. Trudinger, Indiana Univ. Math. J., 20, (1970/71), 1077--1092.
Mathematical Reviews (MathSciNet):
MR301504
Digital Object Identifier: doi:10.1512/iumj.1971.20.20101
G. D. Mostow, Quasi-conformal mappings in $n$-space and the rigidity of hyperbolic space forms, Inst. Hautes Études Sci. Publ. Math., (34) (1968), 53--104.
Mathematical Reviews (MathSciNet):
MR236383
Digital Object Identifier: doi:10.1007/BF02684590
P. Poggi-Corradini and K. Rajala, An egg-yolk principle and exponential integrability for quasiregular mappings, J. London Math. Soc. (2), 76(2) (2007), 531--544.
Mathematical Reviews (MathSciNet):
MR2363431
Digital Object Identifier: doi:10.1112/jlms/jdm078
Nagoya Mathematical Journal
