The Pohozaev Identity for the Fractional Laplacian

Andrews G.E., Askey R., Roy R.: Special Functions. Cambridge University Press, Cambridge (2000)

Berndt B.C.: Ramanujan’s Notebooks, Part II. Springer, Berlin (1989)

Bogdan K., Grzywny T., Ryznar M.: Heat kernel estimates for the fractional Laplacian with Dirichlet conditions. Ann. Probab. 38, 1901–1923 (2010)

Brandle C., Colorado E., de Pablo A.: A concave-convex elliptic problem involving the fractional Laplacian. Proc. R. Soc. Edinb. Sect. A 143, 39–71 (2013)

Cabré X., Cinti E.: Sharp energy estimates for nonlinear fractional diffusion equations. Calc. Var. Partial Differ. Equ. 49, 233–269 (2014)

Cabré X., Tan J.: Positive solutions of nonlinear problems involving the square root of the Laplacian. Adv. Math. 224, 2052–2093 (2010)

Caffarelli L., Roquejoffre J.M., Sire Y.: Variational problems in free boundaries for the fractional Laplacian. J. Eur. Math. Soc. 12, 1151–1179 (2010)

Caffarelli L., Silvestre L.: Regularity theory for fully nonlinear integro-differential equations. Commun. Pure Appl. Math. 62, 597–638 (2009)

Caffarelli L., Silvestre L.: An extension problem related to the fractional Laplacian. Commun. Partial Differ. Equ. 32, 1245–1260 (2007)

Chen W., Li C., Ou B.: Classification of solutions to an integral equation. Commun. Pure Appl. Math. 59, 330–343 (2006)

Evans, L.C., Gariepy, R.F.: Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics. CRC Press, Boca Raton (1992)

Fall M.M., Weth T.: Nonexistence results for a class of fractional elliptic boundary value problems. J. Funct. Anal. 263, 2205–2227 (2012)

Getoor R.K.: First passage times for symmetric stable processes in space. Trans. Am. Math. Soc. 101, 75–90 (1961)

de Pablo, A., Sánchez, U.: Some Liouville-type results for a fractional equation. Preprint

Pohozaev S.I.: On the eigenfunctions of the equation Δu + λf(u) =  0. Dokl. Akad. Nauk SSSR 165, 1408–1411 (1965)

Ros-Oton X., Serra J.: Fractional Laplacian: Pohozaev identity and nonexistence results. C. R. Math. Acad. Sci. Paris 350, 505–508 (2012)

Ros-Oton X., Serra J.: The Dirichlet problem for the fractional Laplacian: regularity up to the boundary. J. Math. Pures Appl. 101, 275–302 (2014)

Servadei R., Valdinoci E.: Mountain pass solutions for non-local elliptic operators. J. Math. Anal. Appl. 389, 887–898 (2012)