Solutions To Dirichlet Problem And Neumann Problem

The complete set of this project focuses on solvability of the Dirichlet problem of therntypern_rnΔ_ = u=f __ Ωrn_ = u _Ωrnrnand the Neumann problem of the typern_rnΔ_ = u __ Ωrn__rn__ = ℎ __ _Ωrn.rnThe explicit solutions of the problem in particular when _ = 0, in elliptic linear operatorrnspecifically in Laplace’s operator and also discuss the integral representation for the solution ofrnthe Dirichlet problem for harmonic functions in upper half space and in a ball in the wholernof ℝ_.rnKeywords Ball, Dirichlet problem, half space, harmonic functions, integral representation,rnNeumann problem

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