2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70614It is shown that the non-homogeneous Dirichlet and Neuman problems for the $2^{nd}$-order Seiberg-Witten equation admit a regular solution once the $\mathcal{H}$-condition (described in the article) is satisfied. The approach consist in applying the elliptic techniques to the variational setting of the Seiberg-Witten equation.19 pagesAnalysis of PDEsMathematical PhysicsDifferential Geometry58J05; 58E50text