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.

Other Information: 

10th Anniversary Speaker Series 2007