On the tangential gradient of the kernel of the double layer potential
Massimo Lanza de Cristoforis · Complex Variables and Elliptic Equations · 2024
In this paper, we consider an elliptic operator with constant coefficients and we estimate the maximal function of the tangential gradient of the kernel of the double layer potential with respect to its first variable. As a consequence, we deduce the validity of a continuity property of the double layer potential in Hölder spaces on the boundary that extends previous results for the Laplace operator and for the Helmholtz operator.