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Nonlocal problems for some partial differential equations. (English) Zbl 0771.35012

Summary: Nonlocal problems for polyharmonic functions and for a special third order system in a half plane are studied which have applications in elasticity. Some of them are solved explicitly on the basis of solutions to related classical problems, others are reduced to the Riemann problem for several holomorphic functions.

MSC:

35G15 Boundary value problems for linear higher-order PDEs
31B30 Biharmonic and polyharmonic equations and functions in higher dimensions
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
30E25 Boundary value problems in the complex plane
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References:

[1] Bitsadze A.V., Dokl. Akad. Nauk SSSR 185 pp 739– (1969)
[2] Bitsadze A.V., Boundary value problems of elliptic equations of second order (1986)
[3] Gakhov F.D., Equations of convolution type (1978) · Zbl 0458.45002
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[9] DOI: 10.1002/zamm.19680480612 · Zbl 0167.10001 · doi:10.1002/zamm.19680480612
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