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On the optimal local regularity for gauge field theories. (English) Zbl 0940.35011

The authors present the main estimates which allow to prove local well-posedness in \(H^s\), \(s>(n-2)/2\), in the case of the Maxwell-Klein-Gordon equations in \(n+1\) dimensions, \(n\geq 4\). For simplicity the relevance of these estimates is demonstrated for a model problem which exhibits all the main difficulties encountered in the Maxwell-Klein-Gordon equations relative to the Coulomb gauge.

MSC:

35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
35L10 Second-order hyperbolic equations
35B65 Smoothness and regularity of solutions to PDEs
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