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Bergman Kernel Approach

In: Methods of Mathematical Physics

Author

Listed:
  • Alexey N. Karapetyants

    (Southern Federal University, Institute of Mathematics, Mechanics and Computer Sciences and Regional Mathematical Center)

  • Vladislav V. Kravchenko

    (Cinvestav-IPN, Campus Queretaro, Department of Mathematics)

Abstract

The aim of this chapter is to introduce and explain an extremely useful tool for practical solution of boundary value and spectral problems for elliptic equations of mathematical physics. Originally developed in Bergman and Schiffer, Kernel Functions and Elliptic Differential Equations in Mathematical Physics (Academic Press, New York, 1953), it received relatively little attention in bibliography, though its range of applicability is not inferior to that of Green’s function, and moreover, the concept of the complete system of solutions acquires even more profound meaning when viewed through the prism of the Bergman kernel approach that we shall study in this chapter.

Suggested Citation

  • Alexey N. Karapetyants & Vladislav V. Kravchenko, 2022. "Bergman Kernel Approach," Springer Books, in: Methods of Mathematical Physics, chapter 0, pages 385-398, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-17845-0_16
    DOI: 10.1007/978-3-031-17845-0_16
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