Abstract
AbstractWe prove the validity of regularizing properties of the boundary integral operator corresponding to the double layer potential associated to the fundamental solution of a nonhomogeneous second order elliptic differential operator with constant coefficients in Hölder 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 kernels of integral operators and a generalization of a result for integral operators on differentiable manifolds.
Funder
Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Reference34 articles.
1. Chavel, I.: Eigenvalues in Riemannian Geometry. Including a Chapter by Burton Randol. With an Appendix by Jozef Dodziuk. Pure and Applied Mathematics, vol. 115. Academic Press, Inc., Orlando (1984)
2. Chkadua, O.: Personal communication (2023)
3. Cialdea, A.: A general theory of hypersurface potentials. Ann. Mat. 168, 37–61 (1995)
4. Colton, D., Kress, R.: Integral Equation Methods in Scattering Theory. Wiley, New York (1983)
5. Dalla Riva, M.: A family of fundamental solutions of elliptic partial differential operators with real constant coefficients. Integr. Equ. Oper. Theory 76, 1–23 (2013)
Cited by
4 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献