Cauchy's problem for a class of fourth order elliptic equations in two independent variables

Abstract

Integral operator techniques are used to construct the solution to Cauchy's problem for a class of fourth order elliptic equations in two independent variables. If the Cauchy data is prescribed along an arbitrary analytic arc C, then approximate solutions can be obtained on compact subsets of domains which are conformally symmetric with respect to C. This improves upon results previously obtained by Henrici, Pucci, and Colton.

^†This research was supported by a Summer Faculty Fellowship at Indiana University

^†This research was supported by a Summer Faculty Fellowship at Indiana University

Notes

^†This research was supported by a Summer Faculty Fellowship at Indiana University