Sets of uniqueness for inframonogenic functions

As a consequence of the maximum principle, it is obvious that one sphere is a set of uniqueness for harmonic functions. This means that any harmonic function in a domain Ω ⊂ Rm, which vanishes on a sphere contained together with its interior in Ω, is identical to zero there. Inframonogenic functions are the solutions of the equation ∂f ∂ = 0 and recently it became clear that they have interesting connections with some topics of linear elasticity theory.
The aim of this talk is to show how, even in absence of the maximum principle, a sphere is a set of uniqueness for inframonogenic functions in Euclidean spaces of odd dimension. In even dimension we provide examples of non-zero inframonogenic functions which vanish on a sphere.
Joint work with: A. Moreno García, T. Moreno García.