Dumitru Motreanu, Nicolae Tarfulea
Abstract:
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.
Show me the PDF file (269 KB), TEX file, and other files for this article.
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 |
Return to the EJDE web page