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UNIQUENESS PROPERTIES OF SOLUTIONS TO SCHRODINGER EQUATIONS
 

Summary: UNIQUENESS PROPERTIES OF SOLUTIONS TO
SCHRšODINGER EQUATIONS
L. ESCAURIAZA, C. E. KENIG, G. PONCE, AND L. VEGA
1. Introduction
To place the subject of this paper in perspective, we start out with a brief
discussion of unique continuation. Consider solutions to
(1.1) u(x) =
n
j=1
2
u
x2
j
(x) = 0,
(harmonic functions) in the unit ball {x Rn
: |x| < 1}. When n = 2, these func-
tions are real parts of holomorphic functions, and so, if they vanish of infinite order
at x = 0, they must vanish identically. We call this the strong unique continuation
property (s.u.c.p.). The same result holds for n > 2, since harmonic functions are
still real analytic in {x Rn

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics