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Boundary Value Problems and Boundary Integral Operators

In: Singularly Perturbed Boundary Value Problems

Author

Listed:
  • 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)

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).

Suggested Citation

  • Matteo Dalla Riva & Massimo Lanza de Cristoforis & Paolo Musolino, 2021. "Boundary Value Problems and Boundary Integral Operators," Springer Books, in: Singularly Perturbed Boundary Value Problems, chapter 0, pages 179-221, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-76259-9_6
    DOI: 10.1007/978-3-030-76259-9_6
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