Differential and Integral Equations

Local asymptotic nondegeneracy for multi-bubble solutions to the biharmonic Liouville-Gel'fand problem in dimension four

Hiroshi Ohtsuka and Futoshi Takahashi

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Abstract

We consider the biharmonic Liouville-Gel'fand problem under the Navier boundary condition in four space dimension. Under the nondegeneracy assumption of blow up points of multiple blowing-up solutions, we prove several estimates for the linearized equations and obtain some convergence result. The result can be seen as a weaker version of the asymptotic nondegeneracy of multi-bubble solutions, which was recently established by Grossi-Ohtsuka-Suzuki in two-dimensional Laplacian case.

Article information

Source
Differential Integral Equations, Volume 28, Number 7/8 (2015), 801-822.

Dates
First available in Project Euclid: 11 May 2015

Permanent link to this document
https://projecteuclid.org/euclid.die/1431347864

Mathematical Reviews number (MathSciNet)
MR3345334

Zentralblatt MATH identifier
1363.35104

Subjects
Primary: 35J30: Higher-order elliptic equations [See also 31A30, 31B30] 35J35: Variational methods for higher-order elliptic equations 35B40: Asymptotic behavior of solutions

Citation

Ohtsuka, Hiroshi; Takahashi, Futoshi. Local asymptotic nondegeneracy for multi-bubble solutions to the biharmonic Liouville-Gel'fand problem in dimension four. Differential Integral Equations 28 (2015), no. 7/8, 801--822. https://projecteuclid.org/euclid.die/1431347864


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