Abstract
Using the properties of iterated potentials, the Venttsel problem for the Laplace and Helmholtz equations is reduced to the Fredholm equation. The possibility of applying the iterated potentials in studies of the Helmholtz equation with boundary conditions of higher orders is shown. Bibliography: 7 titles.
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References
A. D. Venttsel, “On boundary conditions for multidimensional diffusion processes,”Teor. Veroyatn. Primen.,4, No. 2, 172–185 (1959).
D. E. Apushkinskaya and A. I. Nazarov, “Initial boundary value problem with Venttsel boundary condition for nondivergent parabolic equations,”Algebra Analiz,6, No. 6, 1–29 (1994).
D. E. Apushkinskaya and A. I. Nazarov, “Hölder's estimates of solutions of degenerate boundary Venttsel problems for parabolic and elliptic equations of nondivergent type,”Probl. Mat. Anal.,17, 3–19 (1977).
V. I. Smirnov,A. Course in Higher Mathematics [in Russian], Vol. 4, Part 2, Moscow (1954).
S. G. Mikhlin,Linear Partial Differential Equations [in Russian], Moscow (1977).
A. M. Lyapunov,Collected Works [in Russian], Vol. 1, Moscow (1954).
Yu. D. Burago and V. A. Zalgaller,Introduction to Riemann Geometry [in Russian], St. Petersburg (1994).
Additional information
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 250, 1998, pp. 203–218.
Translated by T. N. Surkova.
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Lukyanov, V.V., Nazarov, A.I. Solving the venttsel problem for the laplace and helmholtz equations with the help of iterated potentials. J Math Sci 102, 4265–4274 (2000). https://doi.org/10.1007/BF02673857
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DOI: https://doi.org/10.1007/BF02673857