SOLUTION OF THE NEUMANN PROBLEM, FOR THE HELMHOLTZ EQUATION, IN THE EXTERIOR OF A SURFACE WITH CORNERS.

Title: SOLUTION OF THE NEUMANN PROBLEM, FOR THE HELMHOLTZ EQUATION, IN THE EXTERIOR OF A SURFACE WITH CORNERS.
Identifier: AAI8119657
identifier: 8119657
Creator: HARRIS, WHITNEY STEWART, JR.
Contributor: Richard Sacksteder
Date: 1981
Language: English
Publisher: City University of New York.
Subject: Mathematics
Abstract: In R('3), let (SUMM) be a C('2) manifold with corners. Let E denote the set of.;edges of (SUMM), and let (SUMM) = (SUMM) - E denote the set of open faces of (SUMM). The(' ).;integral equation method is used to solve the Neumann problem for the.;Helmholtz equation in the exterior of (SUMM), under either of the following.;hypotheses: (1) (SUMM) has the property that, near an edge or corner, (SUMM) is.;part of a polyhedron having angle between faces at least 90(DEGREES) or is part of.;a right circular cylinder. The allowable Neumann data functions are in.;C('0) (INTERSECT) L('(INFIN))((SUMM)). (2)All of (SUMM) is smooth (C('2)). The Neumann data functions(' ).;g(p) are in C('0) (INTERSECT) L('2)((SUMM)). They are allowed to grow, in a controlled(' ).;manner, as p approaches curves bounding regions on the surface.;(formerly edges and faces).;Proofs of lemmas about the behavior of single and double layer potentials are also given.
Type: dissertation
Source: PQT Legacy CUNY.xlsx
degree: Ph.D.
Program: Mathematics

Media: SOLUTION OF THE NEUMANN PROBLEM, FOR THE HELMHOLTZ EQUATION, IN THE EXTERIOR OF A SURFACE WITH CORNERS.