Year: 2017
Author: Xiaomeng Li
Journal of Partial Differential Equations, Vol. 30 (2017), Iss. 1 : pp. 64–75
Abstract
Let N≥2, αN=Nω1/(N−1)N−1, where ωN−1 denotes the area of the unit sphere in RN. In this note, we prove that for any $0<\alpha
supu∈W1,N(RN),‖u‖W1,N(RN)≤1∫RN|u|β(eα|u|NN−1−N−2∑j=0αjj!|u|NjN−1)dx
can be attained by some function u∈W1,N(RN) with ‖u‖W1,N(RN)=1. Moreover, when α≥αN, the above supremum is infinity.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v30.n1.5
Journal of Partial Differential Equations, Vol. 30 (2017), Iss. 1 : pp. 64–75
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Extremal function