Accession Number:

AD0272698

Title:

REFLECTION OF BIHARMONIC FUNCTIONS ACROSS ANALYTIC BOUNDARY CONDITIONS

Descriptive Note:

Corporate Author:

CALIFORNIA UNIV BERKELEY

Personal Author(s):

Report Date:

1961-12-01

Pagination or Media Count:

1.0

Abstract:

The reflection of solutions of a biharmonic equation across an analytic arc satisfies two analytic boundary conditions. More specifically but without stating all hypotheses, if a biharmonic function is given on a simply connected open set, partially bounded by an analytic arc without end points, and satisfies two analytic boundary conditions, then there exists a simply connected region containing the analytic arc in its interior, and a unique function biharmonic on this region, which agrees with the biharmonic function. There are two cases treated. In the first case, linear boundary conditions with analytic coefficients are given and a condition on the coefficients is stated. In the second case, nonlinear boundary conditions are given, and a condition is stated, which when satisfied, permits reflection locally. The conditions in the linear case will cover, among other things, the boundary conditions of the first and second fundamental boundary value problems of elasticity as well as the fundamental mixed boundary value problems in elasticity. Author

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Distribution Statement:

APPROVED FOR PUBLIC RELEASE