Håkan Hedenmalm: On the uniqueness theorem of Holmgren

Abstract: We review Holmgren's classical theorem (1901) in the context of powers of
the Laplacian and a an arc of a curve. We then formulate global Holmgren-type problems
with reduced flatness on the arc, and find that rather often, a lower degree of flatness
is sufficient to have Holmgren's assertion that the solution vanishes identically. This is not
possible in the local context, as a consequence of the Cauchy-Kovalevskaya theorem.