Extremal functions for Moser's inequality
Author:
KaiChing Lin
Journal:
Trans. Amer. Math. Soc. 348 (1996), 26632671
MSC (1991):
Primary 49J10
MathSciNet review:
1333394
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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 CarlesonChang (1986, is a ball in any dimension) and Flucher (1992, is any domain in 2dimensions).
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Additional Information
KaiChing Lin
Affiliation:
Department of Mathematics, University of Alabama, Tuscaloosa, Alabama 35487
Email:
klin@ua1vm.ua.edu
DOI:
http://dx.doi.org/10.1090/S0002994796015413
PII:
S 00029947(96)015413
Received by editor(s):
January 25, 1995
Received by editor(s) in revised form:
May 30, 1995
Article copyright:
© Copyright 1996
American Mathematical Society
