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Function Spaces and Partial Differential EquationsVolume 2: Contemporary Analysis$
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Ali Taheri

Print publication date: 2015

Print ISBN-13: 9780198733157

Published to Oxford Scholarship Online: September 2015

DOI: 10.1093/acprof:oso/9780198733157.001.0001

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Layered Potentials, Jump Relations and Existence Theorems

Layered Potentials, Jump Relations and Existence Theorems

Chapter:
(p.799) 19 Layered Potentials, Jump Relations and Existence Theorems
Source:
Function Spaces and Partial Differential Equations
Author(s):

Ali Taheri

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198733157.003.0019

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

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