English

Classes of kernels and continuity properties of the double layer potential in H\"{o}lder spaces

Analysis of PDEs 2023-07-12 v1

Abstract

We prove the validity of regularizing properties of the boundary integral operator corresponding to the double layer potential associated to the fundamental solution of a {\em nonhomogeneous} second order elliptic differential operator with constant coefficients in H\"{o}lder spaces by exploiting an estimate on the maximal function of the tangential gradient with respect to the first variable of the kernel of the double layer potential and by exploiting specific imbedding and multiplication properties in certain classes of integral operators and a generalization of a result for integral operators on differentiable manifolds.

Keywords

Cite

@article{arxiv.2307.04775,
  title  = {Classes of kernels and continuity properties of the double layer potential in H\"{o}lder spaces},
  author = {M. Lanza de Cristoforis},
  journal= {arXiv preprint arXiv:2307.04775},
  year   = {2023}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2305.19672, arXiv:2103.06971, arXiv:2307.04153