All functions are locally $s$-harmonic up to a small error

All functions are locally s - harmonic up to a small error

We show that we can approximate every function f ∈ C(B1) with a s-harmonic function in B1 that vanishes outside a compact set. That is, s-harmonic functions are dense in C loc. This result is clearly in contrast with the rigidity of harmonic functions in the classical case and can be viewed as a purely nonlocal feature.

A characterization of a pomonoid $S$ all of its cyclic $S$-posets are regular injective

This work is devoted to give a charcaterization of a pomonoid $S$ such that all cyclic $S$-posets are regular injective.

Harmonic functions in non-locally convex spaces

Jacobi Fields along Harmonic 2 - Spheres in S 3 and S 4 Are Not All Integrable

In a previous paper, we showed that any Jacobi field along a harmonic map from the 2-sphere to the complex projective plane is integrable (i.e., is tangent to a smooth variation through harmonic maps). In this paper, in contrast, we show that there are (non-full) harmonic maps from the 2-sphere to the 3-sphere and 4sphere which have non-integrable Jacobi fields. This is particularly surprising ...

A lower estimate of harmonic functions

We shall give a lower estimate of harmonic‎ ‎functions of order greater than one in a half space‎, ‎which‎ ‎generalize the result obtained by B‎. ‎Ya‎. ‎Levin in a half plane‎.