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The integral representation for a solution of the 2‐d Dirichlet problem with boundary data on closed and open curves
Author(s) -
Krutitskii P. A.
Publication year - 2000
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300015941
Subject(s) - mathematics , dirichlet integral , fredholm integral equation , mathematical analysis , integral equation , dirichlet problem , representation (politics) , boundary (topology) , harmonic function , dirichlet distribution , harmonic , fredholm theory , boundary value problem , pure mathematics , dirichlet's principle , physics , quantum mechanics , politics , political science , law
The integral representation for the solution of the 2‐D Dirichlet problem for harmonic functions with boundary data on closed and open curves is obtained. The solution is expressed as a sum of potentials, the density of which obeys the uniquely solvable Fredholm integral equation of the second kind.