Extremal functions for Moser's inequality

Author:
Kai-Ching Lin

Journal:
Trans. Amer. Math. Soc. **348** (1996), 2663-2671

MSC (1991):
Primary 49J10

MathSciNet review:
1333394

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a bounded smooth domain in , and a function with compact support in . Moser's inequality states that there is a constant , depending only on the dimension , such that

where is the Lebesgue measure of , and the surface area of the unit ball in . We prove in this paper that there are extremal functions for this inequality. In other words, we show that the

is attained. Earlier results include Carleson-Chang (1986, is a ball in any dimension) and Flucher (1992, is any domain in 2-dimensions).

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Additional Information

**Kai-Ching Lin**

Affiliation:
Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487

Email:
klin@ua1vm.ua.edu

DOI:
http://dx.doi.org/10.1090/S0002-9947-96-01541-3

Received by editor(s):
January 25, 1995

Received by editor(s) in revised form:
May 30, 1995

Article copyright:
© Copyright 1996
American Mathematical Society