Boundary Value Problems and Boundary Integral Operators

Matteo Dalla Riva, Massimo Lanza de Cristoforis and Paolo Musolino
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Matteo Dalla Riva: The University of Tulsa, College of Engineering and Natural Science
Massimo Lanza de Cristoforis: Università degli Studi di Padova, Dipartimento di Matematica
Paolo Musolino: Università Ca’ Foscari Venezia, Dipartimento di Scienze Molecolari e Nanosistemi

Chapter Chapter 6 in Singularly Perturbed Boundary Value Problems, 2021, pp 179-221 from Springer

Abstract: Abstract In this chapter we show the existence of solutions to the basic boundary value problems for the Laplace equation using a classical approach based on Potential Theory. Specifically, we consider the Dirichlet problem, the Neumann problem, the Robin problem, the transmission problem, and a mixed problem. To do so, we carry out an analysis of the boundary integral operators associated with the single and double layer potentials in a Schauder space setting. Our presentation of the topic stems from that of Folland (Introduction to partial differential equations. Princeton University Press, Princeton, NJ, second edition, 1995, Chap. 3).

Date: 2021
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DOI: 10.1007/978-3-030-76259-9_6

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