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Sharp Exponential Integrability for Traces of Monotone Sobolev Functions

Published online by Cambridge University Press:  11 January 2016

Pekka Pankka ,
Pietro Poggi-Corradini  and
Kai Rajala
Pekka Pankka
Affiliation:
Department of Mathematics University of Michigan, Ann Arbor, MI 48109, USA, [email protected]
Pietro Poggi-Corradini
Affiliation:
Department of Mathematics Cardwell Hall Kansas State University, Manhattan, KS 66506, USA, [email protected]
Kai Rajala
Affiliation:
Department of Mathematics and Statistics, P. O. Box 35 (MaD), FI-40014, Univ. of Jyväskylä, Finland, [email protected]
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Abstract

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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.

Keywords

46E3531C45
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 192 , 2008 , pp. 137 - 149
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2008

References

[1] Chang, S.-Y. A. and Marshall, D. E., On a sharp inequality concerning the Dirichlet integral, Amer. J. Math., 107(5) (1985), 1015–1033.CrossRefGoogle Scholar
[2] Evans, L. C. and Gariepy, R. F., Measure theory and fine properties of functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992.Google Scholar
[3] Fuglede, B., Extremal length and functional completion, Acta Math., 98 (1957), 171–219.Google Scholar
[4] Gehring, F. W., Symmetrization of rings in space, Trans. Amer. Math. Soc., 101 (1961), 499–519.Google Scholar
[5] Gehring, F. W., Rings and quasiconformal mappings in space, Trans. Amer. Math. Soc., 103 (1962), 353–393.Google Scholar
[6] Heinonen, J., Kilpeläinen, T., and Martio, O., Nonlinear potential theory of degenerate elliptic equations, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, 1993.Google Scholar
[7] Malý, J., Swanson, D., and Ziemer, W. P., The co-area formula for Sobolev mappings, Trans. Amer. Math. Soc., 355(2) (2003), 477–492 (electronic).Google Scholar
[8] Manfredi, J. J., Weakly monotone functions, J. Geom. Anal., 4(3) (1994), 393–402.CrossRefGoogle Scholar
[9] Marshall, D. E., A new proof of a sharp inequality concerning the Dirichlet integral, Ark. Mat., 27(1) (1989), 131–137.Google Scholar
[10] Moser, J., A sharp form of an inequality by N. Trudinger, Indiana Univ. Math. J., 20, (1970/71), 1077–1092.Google Scholar
[11] Mostow, G. D., Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms, Inst. Hautes Études Sci. Publ. Math., (34) (1968), 53–104.Google Scholar
[12] Poggi-Corradini, P. and Rajala, K., An egg-yolk principle and exponential integrability for quasiregular mappings, J. London Math. Soc. (2), 76(2) (2007), 531–544.Google Scholar