# Layered Potentials, Jump Relations and Existence Theorems

# Layered Potentials, Jump Relations and Existence Theorems

This chapter includes a thorough and detailed discussion of existence theorems for the four basic boundary-value problems associated with the Laplace operator, i.e., the interior and exterior Dirichlet problems and the interior and exterior Neumann problems. The theory of integral equations and compact operators play a pivotal role.

*Keywords:*
double layer potential, single layer potentials, jump relations, existence theorems, weakly singular kernels, Cauchy integral operator, Kodaira-Stone-Titchmarsh-Weyl formula

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .