no. 6
On fractional Laplacians – 2
Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 6, pp. 1667-1673.

For s>−1 we compare two natural types of fractional Laplacians (−Δ)s, namely, the “Navier” and the “Dirichlet” ones.

DOI : 10.1016/j.anihpc.2015.08.001
Classification : 47A63, 35A23
Mots clés : Fractional Laplacians, Nonlocal differential operators, Sobolev spaces 
@article{AIHPC_2016__33_6_1667_0,
     author = {Musina, Roberta and Nazarov, Alexander I.},
     title = {On fractional {Laplacians} {\textendash} 2},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1667--1673},
     publisher = {Elsevier},
     volume = {33},
     number = {6},
     year = {2016},
     doi = {10.1016/j.anihpc.2015.08.001},
     mrnumber = {3569246},
     zbl = {1358.47030},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpc.2015.08.001/}
}
TY  - JOUR
AU  - Musina, Roberta
AU  - Nazarov, Alexander I.
TI  - On fractional Laplacians – 2
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2016
SP  - 1667
EP  - 1673
VL  - 33
IS  - 6
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpc.2015.08.001/
DO  - 10.1016/j.anihpc.2015.08.001
LA  - en
ID  - AIHPC_2016__33_6_1667_0
ER  - 
%0 Journal Article
%A Musina, Roberta
%A Nazarov, Alexander I.
%T On fractional Laplacians – 2
%J Annales de l'I.H.P. Analyse non linéaire
%D 2016
%P 1667-1673
%V 33
%N 6
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpc.2015.08.001/
%R 10.1016/j.anihpc.2015.08.001
%G en
%F AIHPC_2016__33_6_1667_0
Musina, Roberta; Nazarov, Alexander I. On fractional Laplacians – 2. Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 6, pp. 1667-1673. doi : 10.1016/j.anihpc.2015.08.001. http://www.numdam.org/articles/10.1016/j.anihpc.2015.08.001/

[1] Alvarado, R.; Brigham, D.; Maz'ya, V.; Mitrea, M.; Ziadé, E. On the regularity of domains satisfying a uniform hour-glass condition and a sharp version of the Hopf–Oleinik boundary point principle, Probl. Mat. Anal., Volume 57 (2011), pp. 3–68 (in Russian); English transl.: J. Math. Sci., 176, 2011, 281–360 | MR | Zbl

[2] Cabré, X.; Sire, Y. Nonlinear equations for fractional Laplacians. I: regularity, maximum principles, and Hamiltonian estimates, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, Volume 31 (2014) no. 1, pp. 23–53 | DOI | Numdam | MR | Zbl

[3] Cabré, X.; Tan, J. Positive solutions of nonlinear problems involving the square root of the Laplacian, Adv. Math., Volume 224 (2010) no. 5, pp. 2052–2093 | DOI | MR | Zbl

[4] Caffarelli, L.; Silvestre, L. An extension problem related to the fractional Laplacian, Commun. Partial Differ. Equ., Volume 32 (2007) no. 7–9, pp. 1245–1260 | MR | Zbl

[5] Capella, A.; Dávila, J.; Dupaigne, L.; Sire, Y. Regularity of radial extremal solutions for some non-local semilinear equations, Commun. Partial Differ. Equ., Volume 36 (2011) no. 8, pp. 1353–1384 | DOI | MR | Zbl

[6] Musina, R.; Nazarov, A.I. On fractional Laplacians, Commun. Partial Differ. Equ., Volume 39 (2014) no. 9, pp. 1780–1790 | DOI | MR | Zbl

[7] Stinga, P.R.; Torrea, J.L. Extension problem and Harnack's inequality for some fractional operators, Commun. Partial Differ. Equ., Volume 35 (2010) no. 11, pp. 2092–2122 | DOI | MR | Zbl

[8] Triebel, H. Interpolation Theory, Function Spaces, Differential Operators, Deutscher Verlag Wissensch., Berlin, 1978 | MR | Zbl

Cité par Sources :