The Laplacian in a plane infinite angle

  • Vladimir B. Vasil’ev


This section is a “realization” of methods, which are developed in Chapter 9 applied to the Laplacian and contains concrete calculations. Similar [238,239] and more complicated problems [94,134,207,208] were considered earlier by other methods, and as a result, it gave the possibility to obtain the theorem of existence and uniqueness of solution under some restrictions on parameters of functional spaces, size of angle and so on. In this section we have chosen similar functional spaces in which our methods give the possibility to formulate the conditions under fulfilling of which the solution of the posed problem exists and is unique (including explicit construction for solution in terms of Fourier and Mellin transforms). Other approaches one can find in papers which are contained in the list of references from [135].


Linear Algebraic Equation Pseudo Differential Operator Functional Space Residue Theorem Plane Infinite 
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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Vladimir B. Vasil’ev
    • 1
  1. 1.Department of Mathematical AnalysisNovgorod State UniversityNovgorodRussia

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