Density properties for fractional sobolev spaces

Annales Academiae Scientiarum Fennicae Mathematica

Volumn 40, Issue 1, 2015, Pages 235-253

  Fiscella, Alessio ^a   Servadei, Raffaella ^b   Valdinoci, Enrico ^a,c  

^a UNIVERSITY OF MILAN   (Italy)

^b UNIVERSITY OF CALABRIA   (Italy)

^c WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

Author keywords

Density properties; Fractional laplacian; Fractional sobolev spaces; Integrodifferential operators

Indexed keywords

EID: 84921973672     PISSN: 1239629X     EISSN: None     Source Type: Journal    
DOI: 10.5186/aasfm.2015.4009     Document Type: Article

References (33)

1. Adams, R. A.: Sobolev spaces. - Academic Press, New York, 1975.
2. Agmon, S.: Lectures on elliptic boundary value problems. - Mathematical Studies 2, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1965.
3. N. - J. Differential Equations 255:8, 2013, 2340-2362.
4. Autuori, G., and P. Pucci: Existence of entire solutions for a class of quasilinear elliptic equations. - NoDEA Nonlinear Differential Equations Appl. 20:3, 2013, 977-1009.
5. Barles, G., E. Chasseigne, and C. Imbert: On the Dirichlet problem for second-order elliptic integro-differential equations. - Indiana Univ. Math. J. 57:1, 2008, 213-246.
6. Barrios, B., E. Colorado, A. De Pablo, and U. Sanchez: On some critical problems for the fractional Laplacian operator. - J. Differential Equations 252, 2012, 6133-6162.
7. Brezis, H.: Analyse fonctionelle. Théorie et applications. - Masson, Paris, 1983.
8. Cabré, X., and J. Tan: Positive solutions of nonlinear problems involving the square root of the Laplacian. - Adv. Math. 224:5, 2010, 2052-2093.
9. Caffarelli, L., and L. Silvestre: An extension problem related to the fractional Laplacian. Comm. Partial Differential Equations 32:7-9, 2007, 1245-1260.
10. Caffarelli, L., and L. Silvestre: Regularity theory for fully nonlinear integro-differential equations. - Comm. Pure Appl. Math. 62:5, 2009, 597-638.
11. Capella, A.: Solutions of a pure critical exponent problem involving the half-Laplacian in annular-shaped domains. - Commun. Pure Appl. Anal. 10:6, 2011, 1645-1662.
12. Di Nezza, E., G. Palatucci, and E. Valdinoci: Hitchhiker's guide to the fractional Sobolev spaces. - Bull. Sci. Math. 136:5, 2012, 521-573.
13. Dipierro, S., O. Savin, and E. Valdinoci: All functions are locally s-harmonic up to a small error. - Preprint, http://arxiv.org/pdf/1404.3652v1.pdf.
14. p-estimates for a class of non-local elliptic equations. - J. Funct. Anal. 262:3, 2012, 1166-1199.
15. Felmer, P., A. Quaas, and J. Tan: Positive solutions of nonlinear Schrödinger equation with the fractional Laplacian. - Proc. Roy. Soc. Edinburgh Sect. A 142:6, 2012, 1237-1262.
16. Fiscella, A.: Saddle point solutions for non-local elliptic operators. - Topol. Methods Nonlinear Anal. (to appear).
17. Folland, G. B.: Real analysis. Modern techniques and their applications. - J. Wiley, New York, 1984.
18. Grisvard, P.: Elliptic problems in nonsmooth domains. - Pitman, Boston, 1985.
19. McLean, W.: Strongly elliptic systems and boundary integral equations. - Cambridge Univ. Press, Cambridge, 2000.
20. Molica Bisci, G.: Fractional equations with bounded primitive. - Appl. Math. Lett. 27, 2014, 53-58.
21. Molica Bisci, G., and R. Servadei: A bifurcation result for nonlocal fractional equations. Anal. Appl. (to appear).
22. Ros-Oton, X., and J. Serra: Fractional Laplacian: Pohozaev identity and nonexistence results. - C. R. Math. Acad. Sci. Paris 350:9-10, 2012, 505-508.
23. Ros-Oton, X. and J. Serra: The Pohozaev identity for the fractional Laplacian. - Arch. Ration. Mech. Anal. 213:2, 2014, 587-628.
24. Servadei, R.: The Yamabe equation in a non-local setting. - Adv. Nonlinear Anal. 2, 2013, 235-270.
25. Servadei, R., and E. Valdinoci: Mountain pass solutions for non-local elliptic operators. - J. Math. Anal. Appl. 389, 2012, 887-898.
26. Servadei, R., and E. Valdinoci: Variational methods for non-local operators of elliptic type. - Discrete Contin. Dyn. Syst. 33:5, 2013, 2105-2137.
27. Servadei, R., and E. Valdinoci: A Brezis-Nirenberg result for non-local critical equations in low dimension. - Commun. Pure Appl. Anal. 12:6, 2013, 2445-2464.
28. Servadei, R., and E. Valdinoci: On the spectrum of two different fractional operators. - Proc. Roy. Soc. Edinburgh Sect. A 144, 2014, 831-855.
29. Servadei, R., and E. Valdinoci: The Brezis-Nirenberg result for the fractional Laplacian. - Trans. Amer. Math. Soc. (to appear).
30. Servadei, R., and E. Valdinoci: Fractional Laplacian equations with critical Sobolev exponent. - Preprint, http://www.math.utexas.edu/mp_arc-bin/mpa?yn=12-58.
31. Silvestre, L.: Regularity of the obstacle problem for a fractional power of the Laplace operator. - PhD Thesis, University of Texas at Austin, http://math.uchicago.edu/~luis/preprints/luisdissreadable.pdf, 2005.
32. Stinga, P. R., and Torrea, J. L.: Extension problem and Harnack's inequality for some fractional operators. - Commun. Partial Differ. Equations 35:10-12, 2010, 2092-2122.
33. Tan, J.: The Brezis-Nirenberg type problem involving the square root of the Laplacian. - Calc. Var. Partial Differential Equations 36:1-2, 2011, 21-41.