Extension theorems for solutions to over-determined systems of partial differential equations
Krueger, Joe Elgin
Wells, Raymond O., Jr.
Master of Arts
Ehrenpreis has shown that, under suitable conditions, an infinitely differentiable solution to an overdetermined system of linear partial differentiable operators with constant coefficients has an extension across the bounded part of the complement of an annular region. It it shown in this thesis that a similar result holds for distribution solutions. Necessary and sufficient conditions for such extension are discussed and several theorems are also given on the extension problem for solutions to one differential operator.