Boundary Value Problems
Volume 2005 (2005), Issue 1, Pages 73-91
Boundary value problems for the nd-order Seiberg-Witten
Departamento de Matemática, Universidade Federal de Santa Catarina, Campus Universitario, Trindade 88040900 Florianópolis - SC, Brazil
Received 8 June 2004
Copyright © 2005 Celso Melchiades Doria. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
It is shown that the nonhomogeneous Dirichlet and Neuman
problems for the nd-order Seiberg-Witten equation on a compact -manifold admit a regular solution once the nonhomogeneous Palais-Smale condition
The approach consists in applying the elliptic techniques to the
variational setting of the Seiberg-Witten equation. The gauge
invariance of the functional allows to restrict the problem to the
Coulomb subspace of configuration space. The coercivity of the -functional, when restricted
into the Coulomb subspace, imply the existence of a weak solution. The regularity then follows from the boundedness of -norms
of spinor solutions and the gauge fixing lemma.