Electron. J. Diff. Equ., Vol. 2009(2009), No. 138, pp. 1-13.

Quasilinear differential equations in exterior domains with nonlinear boundary conditions and application

Dumitru Motreanu, Nicolae Tarfulea

We investigate the existence of weak solutions to a class of quasilinear elliptic equations with nonlinear Neumann boundary conditions in exterior domains. Problems of this kind arise in various areas of science and technology. An important model case related to the initial data problem in general relativity is presented. As an application of our main result, we deduce the existence of the conformal factor for the Hamiltonian constraint in general relativity in the presence of multiple black holes. We also give a proof for uniqueness in this case.

Submitted October 5, 2009. Published October 30, 2009.
Math Subject Classifications: 35J65, 83C05.
Key Words: Quasilinear equation; exterior domain; general relativity; nonlinear boundary conditions; initial data problem; conformal factor.

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Dumitru Motreanu
Département de Mathématiques, Université de Perpignan
66025 Perpignan, France
email: motreanu@univ-perp.fr
Nicolae Tarfulea
Department of Mathematics
Purdue University Calumet, IN 46323, USA
email: tarfulea@calumet.purdue.edu

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