## Asymptotic behavior at infinity of solutions of elliptic equations

- Date: 04/02/2007

Peter Lax (Courant Institute)

University of British Columbia

The prototype problem is the behavior at infinity of all solutions of a

linear elliptic equation that have finite L1 norm in a half cylinder

0<y, x in D,D a smoothly bounded domain. We assume that the

coefficients of the elliptic operator,as well as the boundary

conditions in D, are independent of y. Such a space of solutions can be

abstracted as a linear space K of functions f(y), whose values lie in a

Banach space B, are translation invariant,|f(y)| integrable,and which

are interior compact, an abstract version of ellipticity. We show that

the asymptotic behavior as y tends to infinity of such functions is

given as a sum of exponential functions contained in K.

10th Anniversary Speaker Series 2007