Author:
Abatangelo Nicola,Jarohs Sven
Abstract
AbstractWe show that the first eigenfunction of the fractional Laplacian $${\left( -\Delta \right) }^{s}$$
-
Δ
s
, $$s\in (1/2,1)$$
s
∈
(
1
/
2
,
1
)
, is superharmonic in the unitary ball up to dimension 11. To this aim, we also rely on a computer-assisted step to estimate a rather complicated constant depending on the dimension and the power s.
Funder
Alexander von Humboldt-Stiftung
Publisher
Springer Science and Business Media LLC
Reference18 articles.
1. Abatangelo, N.: Large $$s$$-harmonic functions and boundary blow-up solutions for the fractional Laplacian. Discrete Contin. Dyn. Syst. 3512, 5555–5607 (2015)
2. Abatangelo, N., Valdinoci, E.: Getting acquainted with the fractional Laplacian. Contemporary research in elliptic PDEs and related topics, Springer INdAM Ser. 33, 1–105 (2019)
3. Abramowitz, M., Stegun, I.A.: Handbook of mathematical functions with formulas, graphs, and mathematical tables. National Bureau of Standards Applied Mathematics Series. 55, For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. (1964)
4. Bañuelos, R., DeBlassie, D.: On the first eigenfunction of the symmetric stable process in a bounded Lipschitz domain. Potential Anal. 42(2), 573–583 (2015)
5. Bañuelos, R., Kulczycki, T.: The Cauchy process and the Steklov problem. J. Funct. Anal. 211(2), 355–423 (2004)