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 Lebesgue-Stieltjes 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 Borel-measurable. It is shown that if C has no cusps then the solution of (1) can be obtained in terms of the 'double-layer potential' phi which satisfies the Lebesgue-Stieltjes 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 arc-length on C, and (pi sub s) is a Lebesgue-Stieltjes 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 double-layer 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