Plenary talk
On unique continuation results for discrete partial differential equations
In this talk we discuss how the unique continuation property fails for some discrete elliptic partial differential equations, while it is true for the continuous version of these PDEs under suitable regularity assumptions. As important tools, we present three balls inequalities and logarithmic convexity estimates for discrete magnetic Schrödinger operators and functions posed in the d-dimensional scaled meshed hZ^d. We also comment some results on the evolution case, dealing with the semi-discrete heat equation.
This is a joint work with Angkana Rüland, Aingeru Fernández Bertolin and Luz Roncal.