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Extremals for Moser Inequalities

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Abstract.

This paper shows that extremals exist for four Moser inequalities involving exponential integrals. The results are for Sobolev spaces defined on the spheres S 2 and S 3, on the disk D 2, and on RP 2. The method that Carleson and Chang used for the n-ball, with boundary value zero, can be modified and applied to functions with mean value zero on these domains. This approach also provides an elementary proof of the Moser inequality for S n, n≥2, which is a special case of a result of Fontana.

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Authors and Affiliations

  1. Mathematics Department, Florida International University Miami, Florida, 33199, USA

    S. Hudson & M. Leckband

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  1. S. Hudson
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  2. M. Leckband
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Correspondence to S. Hudson.

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Communicated by P. Rabinowitz

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Hudson, S., Leckband, M. Extremals for Moser Inequalities. Arch. Rational Mech. Anal. 171, 43–54 (2004). https://doi.org/10.1007/s00205-003-0280-7

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  • DOI: https://doi.org/10.1007/s00205-003-0280-7

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