\(L^ p\) estimates of boundary integral equations for some nonlinear boundary value problems

DOI10.1007/BF01385636zbMath0694.65056MaRDI QIDQ909423

Paul P. B. Eggermont, Jukka Saranen

Publication date: 1990

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133512

zbMATH Keywords

stabilityGalerkin methoderror estimatesboundary integral equationcollocation methodsnonlinear boundary conditionspotential problemsLp-spaceuniform boundedness of the inverses of the linearized integral operators

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Nonlinear boundary value problems for linear elliptic equations (35J65) Integral representations of solutions to PDEs (35C15) General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Boundary element methods for boundary value problems involving PDEs (65N38) Boundary value and inverse problems for harmonic functions in two dimensions (31A25)

Related Items

On the convergence of the collocation method for nonlinear boundary integral equations, A BIE method for a nonlinear BVP, Boundary element methods for potential problems with nonlinear boundary conditions, Nonlinear boundary integral equations for harmonic problems, The numerical solution of a nonlinear hypersingular boundary integral equation

Cites Work

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• The convergence of spline collocation for strongly elliptic equations on curves
• The convergence of even degree spline collocation solution for potential problems in smooth domains of the plane
• On the boundary element method for some nonlinear boundary value problems
• Monotone (nonlinear) operators in Hilbert space
• The Lebesgue constants for cardinal spline interpolation
• On the collocation method for a nonlinear boundary integral equation
• The solvability of non-linear functional equations
• Boundary Integral Equation Methods for Solving Laplace's Equation with Nonlinear Boundary Conditions: The Smooth Boundary Case
• Optimal L ∞ Error Estimates for Galerkin Approximations to Solutions of Two-Point Boundary Value Problems
• A Bound on the L ∞ -Norm of L 2 -Approximation by Splines in Terms of a Global Mesh Ratio
• Projection Methods for a Class of Hammerstein Equations