Event № 374
We show that solutions of certain second order elliptic differential equations cannot vanish on the boundary of arbitrarily small domains. Our first example is the Schrodinger equation -Delta u = V(x) u on a bounded domain D of Rn. We show that the measure of D is bounded above by a constant that depends on the Lp norm of V. If D is a slab of Rn, we consider the equation -Delta u = (V(x) + s) u, with V bounded and compactly supported in D. We show that ||V|| is bounded above by a constant that depends on the support of V and the distance of s and the integers. Most of our estimates are optimal in some sense. This is a joint work with J. Edward, S. Hudson, M. Leckband and X. Li from the Florida International University.