On the Boundary Behavior of Solutions to Elliptic and Parabolic Equations—with Applications to Boundary Control for Parabolic Equations

Abstract

It is shown that for bounded domains with infinitely differentiable boundaries solutions of second order elliptic equations (involving infinitely differentiable coefficients), and of the associated parabolic equations, cannot vanish together with their normal derivatives on subsets of the boundary having positive measure. This fact has multiple applications to the boundary control problem for parabolic equations. The results obtained have previously required an analyticity assumption on the boundary and on the coefficients.