Entire $s$-harmonic functions are affine

By M. Fall. 2014

58 citations recorded by the source corpus.

In this paper, we prove that solutions to the equation $(-\Delta)^s u=0$ in $\mathbb{R}^N$, for $s\in (0,1)$, are affine. This will allow us to prove uniqueness of the Riesz potential $|x|^{2s-N}$ in Lebesgue spaces.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/596f54edb63ee186a8dfd9a1a738b162fc7f0960

Citations in the corpus

• Regularity theory for general stable operators (2014, unknown): “For related Liouville theorems, see [14, 13, 10].”