A note on unique continuation for discrete harmonic functions

Abstract

In this note we give a quantitative version of the following simple observation: a discrete harmonic function on the lattice may vanish at each point of a large cube without being zero identically, at the same time there is a version of three balls theorem for discrete harmonic functions since they resemble continuous ones on large scales.

References in corpus (2)

• The stability for the Cauchy problem for elliptic equations
• Uniform stability estimates for the discrete Calderon problems

Cited by in corpus (4)

• The landscape law for tight binding Hamiltonians
• Harmonic functions on the lattice: Absolute monotonicity and propagation of smallness
• On the sharpness of a three circles theorem for discrete harmonic functions
• Approximate Two-Sphere One-Cylinder Inequality in Parabolic Periodic Homogenization