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The Uniquely Solvable Integral Equation for the Harmonic Dirichlet Problem in a Plane Domain with Cuts
Author(s) -
Krutitskii P.A.
Publication year - 1999
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(199909)79:9<591::aid-zamm591>3.0.co;2-w
Subject(s) - fredholm integral equation , mathematics , dirichlet problem , dirichlet integral , integral equation , harmonic function , harmonic measure , mathematical analysis , dirichlet boundary condition , harmonic , dirichlet's energy , dirichlet's principle , domain (mathematical analysis) , plane (geometry) , dirichlet eigenvalue , fredholm theory , boundary (topology) , boundary value problem , geometry , physics , quantum mechanics
The boundary integral equation method is applied to the Dirichlet problem for harmonic functions in a connected plane region with cuts. The problem is reduced to a Fredholm equation of the second kind which is uniquely solvable. In this way the classical solution of the Dirichlet problem is obtained. The solution is unique.