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Critical Dimension of a Hessian Equation Involving Critical Exponent and a Related Asymptotic Result

✍ Scribed by Kai-Seng Chou; Di Geng; Shu-Sen Yan

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
772 KB
Volume
129
Category
Article
ISSN
0022-0396

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✦ Synopsis

Let S k ({ 2 u), 1 k<nΓ‚2, be the k th Hessian operator. We study the problem

where #(k) is the critical exponent for S k and 0 is a ball. Results generalizing those obtained by Brezis Nirenberg for the special case k=1 are established. A discussion on the asymptotic behavior of solutions of the problem (as * Γ„ 0) is also included. 1996 Academic Press, Inc. has been discussed by many authors, including Guedda and Veron [10] and Egnell [6] ( p-Laplace operator), Edmunds et al. [8] (biharmonic operator), Pucci and Serrin [12] (polyharmonic operator), and Chou and Geng [5] (weighted Laplace operator).

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