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Reflecting Solutions of High Order Elliptic Differential Equations in Two Independent Variables Across Analytic ArcsConsideration is given specifically to sixth order elliptic partial differential equations in two independent real variables x, y such that the coefficients of the highest order terms are real constants. It is assumed that the differential operator has distinct characteristics and that it can be factored as a product of second order operators. By analytically continuing into the complex domain and using the complex characteristic coordinates of the differential equation, it is shown that its solutions, u, may be reflected across analytic arcs on which u satisfies certain analytic boundary conditions. Moreover, a method is given whereby one can determine a region into which the solution is extensible. It is seen that this region of reflection is dependent on the original domain of difinition of the solution, the arc and the coefficients of the highest order terms of the equation and not on any sufficiently small quantities; i.e., the reflection is global in nature. The method employed may be applied to similar differential equations of order 2n.
Document ID
19730023750
Acquisition Source
Headquarters
Document Type
Thesis/Dissertation
Authors
Carleton, O. (California Univ. Santa Barbara, CA, United States)
Date Acquired
September 2, 2013
Publication Date
June 1, 1972
Subject Category
Mathematics
Report/Patent Number
NASA-CR-135667
Accession Number
73N32483
Funding Number(s)
CONTRACT_GRANT: NGL-05-010-008
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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