Nonlinear boundary integral equations for harmonic problems. (English) Zbl 0974.65112

Summary: Novel first kind Steklov-Poincaré and hypersingular operator boundary integral equations with nonlinear perturbations are proposed to solve harmonic problems in two- and three-dimensional Lipschitz domains with nonlinear boundary conditions. The equivalence and regularity of the solutions of the formulations are described. To initiate computational procedures for the solution of nonlinear boundary integral equations, a standard Newton scheme is analyzed and corresponding convergence results are given.


65N38 Boundary element methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
31B20 Boundary value and inverse problems for harmonic functions in higher dimensions
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J65 Nonlinear boundary value problems for linear elliptic equations
31A25 Boundary value and inverse problems for harmonic functions in two dimensions


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