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Boundary value problems for thend-order Seiberg-Witten equations

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It is shown that the nonhomogeneous Dirichlet and Neuman problems for thend-order Seiberg-Witten equation on a compact-manifold admit a regular solution once the nonhomogeneous Palais-Smale condition 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 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.

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Correspondence to Celso Melchiades Doria.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Doria, C.M. Boundary value problems for thend-order Seiberg-Witten equations. Bound Value Probl 2005, 412046 (2005). https://doi.org/10.1155/BVP.2005.73

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  • DOI: https://doi.org/10.1155/BVP.2005.73