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Blow-up of solutions
of critical elliptic equations in three dimensions
Rupert L. Frank, Tobias König and Hynek Kovařík |
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Vol. 17 (2024), No. 5, 1633–1692
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Abstract |
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We describe the asymptotic behavior of positive solutions of the equation in with a homogeneous Dirichlet boundary condition. The function is assumed to be critical in the sense of Hebey and Vaugon, and the functions 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 Brezis and Peletier (1989). Similar results are also obtained for solutions of the equation in . |
Keywords
blow-up, critical elliptic equations
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Mathematical Subject Classification
Primary: 35B44, 35J60
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Milestones
Received: 11 August 2021
Revised: 27 July 2022
Accepted: 23 September 2022
Published: 20 June 2024
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Authors |
| Rupert L. Frank | |
| Mathematisches Institut Ludwig-Maximilians-Universitat München München Germany |
Department of Mathematics Caltech Pasadena, CA United States |
| Tobias König | |
| Institut de Mathématiques de
Jussieu Paris Rive Gauche Université de Paris Campus des Grands Moulins Paris France |
Institut für Mathematik Goethe University Frankfurt Frankfurt am Main Germany |
| Hynek Kovařík | |
| DICATAM, Sezione di Matematica Università degli studi di Brescia Brescia Italy |
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| © 2024 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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