Frank, Rupert L. and König, Tobias and Kovařík, Hynek (2021) Blow-up of solutions of critical elliptic equation in three dimensions. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20211004-232817904
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Abstract
We describe the asymptotic behavior of positive solutions uϵ of the equation −Δu + au = 3u^(5−ϵ) in Ω ⊂ ℝ³ with a homogeneous Dirichlet boundary condition. The function a is assumed to be critical in the sense of Hebey and Vaugon and the functions u_ϵ are assumed to be an optimizing sequence for the Sobolev inequality. Under a natural nondegeneracy assumption we derive the exact rate of the blow-up and the location of the concentration point, thereby proving a conjecture of Brézis and Peletier (1989). Similar results are also obtained for solutions of the equation −Δu +(a+ϵV)u = 3u⁵ in Ω.
Item Type: | Report or Paper (Discussion Paper) | ||||||||
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Additional Information: | © 2021 by the authors. This paper may be reproduced, in its entirety, for non-commercial purposes. Partial support through US National Science Foundation grants DMS-1363432 and DMS-1954995 (R.L.F.) and through ANR BLADE-JC ANR-18-CE40-002 (T.K.) is acknowledged. T.K. thanks Paul Laurain for several useful discussions. | ||||||||
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Record Number: | CaltechAUTHORS:20211004-232817904 | ||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20211004-232817904 | ||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||
ID Code: | 111204 | ||||||||
Collection: | CaltechAUTHORS | ||||||||
Deposited By: | George Porter | ||||||||
Deposited On: | 07 Oct 2021 19:10 | ||||||||
Last Modified: | 07 Oct 2021 19:10 |
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