L p estimates of boundary integral equations for some nonlinear boundary value problems

Autor:	J. Saranen, Paul P. B. Eggermont
Rok vydání:	1990
Předmět:	Computational Mathematics Nonlinear system Collocation Applied Mathematics Collocation method Mathematical analysis Uniform boundedness Boundary value problem Galerkin method Lipschitz continuity Integral equation Mathematics
Zdroj:	Numerische Mathematik. 58:465-478
ISSN:	0945-3245 0029-599X
DOI:	10.1007/bf01385636
Popis:	Recently, Galerkin and collocation methods have been analyzed for boundary integral equation formulations of some potential problems in the plane with nonlinear boundary conditions, and stability results and error estimates in theH 1/2-norm have been proved (Ruotsalainen and Wendland, and Ruotsalainen and Saranen). We show that these results extend toL p setting without any extra conditions. These extensions are proved by studying the uniform boundedness of the inverses of the linearized integral operators, and then considering the nonlinear equations. The fact that inH 1/2 setting the nonlinear operator is a homeomorphism with Lipschitz continuous inverse plays a crucial role. Optimal error estimates for the Galerkin and collocation method inL p space then follow.
Databáze:	OpenAIRE
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