Boundary value problems for the 2nd-order Seiberg-Witten equations. (2nd February 2005) - Doria, Celso Melchiades
Abstract : It is shown that the nonhomogeneous Dirichlet and Neuman problems for the2 nd-order Seiberg-Witten equation on a compact4 -manifoldX admit a regular solution once the nonhomogeneous Palais-Smale conditionℋ is satisfied. 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 subspace𝒞 α ℭ of configuration space. The coercivity of the𝒮 𝒲 α -functional, when restricted into the Coulomb subspace, imply the existence of a weak solution. The regularity then follows from the boundedness ofL ∞ -norms of spinor solutions and the gauge fixing lemma.