
Accession Number : AD0726417
Title : The Solution of the Dirichlet Problem for Lapalce's Equation when the Boundary Data is Discontinuous and the Domain has a Boundary which is of Bounded Rotation by Means of the LebesgueStieltjes Integral Equation for the Double Layer Potential.
Descriptive Note : Technical rept.,
Corporate Author : WISCONSIN UNIV MADISON DEPT OF COMPUTER SCIENCES
Personal Author(s) : Cryer,Colin W.
Report Date : AUG 1970
Pagination or Media Count : 143
Abstract : The Dirichlet problem (u sub xx) + (u sub yy) = 0, (x,y) epsilon R; u = g, (x,y) epsilon C; (1) is considered. Here R is a bounded domain in the (x,y)plane with boundary C. C is of 'bounded rotation' and g is bounded and Borelmeasurable. It is shown that if C has no cusps then the solution of (1) can be obtained in terms of the 'doublelayer potential' phi which satisfies the LebesgueStieltjes integral equation (I+T) phi = g/pi. Here (T phi)(s) = the integral over C of (phi(sigma) (Pi sub s) d(sigma)), where s denotes arclength on C, and (pi sub s) is a LebesgueStieltjes measure which depends on C. The case when C has cusps is also considered. The report also contains a lengthy survey of th literature on doublelayer potentials. (Author)
Descriptors : (*BOUNDARY VALUE PROBLEMS, *POTENTIAL THEORY), (*PARTIAL DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION), NUMERICAL ANALYSIS, CONFORMAL MAPPING, INTEGRAL EQUATIONS, WAVE FUNCTIONS, THEOREMS
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE