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In this paper we consider an elliptic operator with constant coefficients andwe estimate the maximal function of the tangential gradient of the kernel ofthe double layer potential with respect to its first variable. As aconsequence, we deduce the validity of a continuity property of the doublelayer potential in H\"{o}lder spaces on the boundary that extends previousresults for the Laplace operator and for the Helmholtz operator.

On the tangential gradient of the kernel of the double layer potential