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The nonlinear boundary value problems for second order elliptic system of class \(E_ 2\) for multiply connected domains in the plane. (English) Zbl 0820.35065

Nonlinear boundary value problems for second order elliptic systems of class \(E\), for multiply connected domains in the plane are considered. We give integral representations of Green’s functions for Dirichlet problems and Neumann problems. By using the Green’s functions, we mainly discuss the solvability of nonlinear Dirichlet problems and Neumann problems and give an expression of the solution.

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
35C15 Integral representations of solutions to PDEs
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