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 Holder spaces on the boundary that extends previous results for the Laplace operator and for the Helmholtz operator.
On the tangential gradient of the kernel of the double layer potential
Lanza de Cristoforis, M.
Writing – Original Draft Preparation
2024
Abstract
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 Holder spaces on the boundary that extends previous results for the Laplace operator and for the Helmholtz operator.
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