Luis Escauriaza

On a regularity theorem for weak solutions to transmission problems with internal Lipschitz boundaries

We show that if u is a weak solution to div(A⊇u)=0 on an open set Ω containing a Lipschitz domain D, where A=kI χD+ I χΩ/D (k>0, k¬=1), then the nontangential maximal function of the gradient of u lies in L 2 (∂D)

Unique continuation for parabolic operators

It is shown that if a functionu satisfies a backward parabolic inequality in an open set Ω∉Rn+1 and vanishes to infinite order at a point (x0·t0) in Ω, thenu(x, t0)=0 for allx in the connected component ofx0 in Ω⌢(Rn×{t0}).

Observability inequalities and measurable sets

This paper presents two observability inequalities for the heat equation over

C1,? domains and unique continuation at the boundary

\Omega\times(0,T)

On Uniqueness Properties of Solutions of Schrödinger Equations

. In the first one, the observation is from a subset of positive measure in

DOUBLING PROPERTIES OF CALORIC FUNCTIONS

\Omega\times(0,T)

Carleman inequalities and the heat operator

, while in the second, the observation is from a subset of positive surface measure in

Regularity properties of solutions to transmission problems

\partial\Omega \times(0,T)

The sharp Hardy uncertainty principle for Schrödinger evolutions

. It also proves the Lebeau-Robbiano spectral inequality when

Bounds for the fundamental solutions of elliptic and parabolic equations

\Omega