Hs versus C0-weighted minimizer

Nonlinear Differential Equations and Applications

Volumn 22, Issue 3, 2015, Pages 477-497

  Iannizzotto, Antonio ^a   Mosconi, Sunra ^b   Squassina, Marco ^a  

^a UNIVERSITY OF VERONA   (Italy)

^b UNIVERSITY OF CATANIA   (Italy)

Author keywords

35P15; 35P30; 35R11

Indexed keywords

EID: 84929836689     PISSN: 10219722     EISSN: 14209004     Source Type: Journal    
DOI: 10.1007/s00030-014-0292-z     Document Type: Article

References (30)

1. Aikawa H., Kipleläinen T., Shanmugalingam N., Zhong X.: Boundary Harnack principle for p-harmonic functions in smooth euclidean spaces. Potential Anal. 26, 281–301 (2007)
2. Barrios, B.; Colorado, E.; Servadei, R.; Soria, F.: A critical fractional equation with concave-convex power nonlinearities. Ann. Inst. H. Poincaré Anal. Non Linéaire (to appear, 2014)
3. Brasco, L.; Franzina, G.: Convexity properties of Dirichlet integrals and Picone-type inequalities. Kodai Math. J. (2014a, to appear)
4. Brasco, L., Lindgren, E., Parini, E.: The fractional Cheeger problem (2014b, preprint)
5. 1 minimizers. C. R. Acad. Sci. Paris. 317, 465–472 (1993)
6. Cabré X., Sire Y.: Nonlinear equations for fractional Laplacians I: regularity, maximum principles, and Hamiltonian estimates. Ann. Inst. Henri Poincaré (C) Nonlinear Anal. 31, 23–53 (2014)
7. Cabré, X.; Sire, Y.: Nonlinear equations for fractional Laplacians II: existence, uniqueness, and qualitative properties of solutions. Trans. Am. Math. Soc. (2014, to appear)
8. Caffarelli L.A.: Nonlocal equations, drifts and games. Nonlinear Partial Differ. Equ. Abel Symposia. 7, 37–52 (2012)
9. Caffarelli L., Silvestre L.: An extension problem related to the fractional Laplacian. Commun. Partial Differ. Equ. 32, 1245–1260 (2007)
10. Caffarelli L., Roquejoffre J.-M., Sire Y.: Variational problems with free boundaries for the fractional Laplacian. J. Eur. Math. Soc. 12, 1151–1179 (2010)
11. Chen W., Li C., Ou B.: Classification of solutions for an integral equation. Commun. Pure Appl. Math. 59, 330–343 (2006)
12. Di Castro, A., Kuusi, T., Palatucci, G.: Local behavior of fractional p-minimizers (2014, preprint)
13. Di Nezza E., Palatucci G., Valdinoci E.: Hitchhiker’s guide to the fractional Sobolev spaces. Bull. Sci. Math. 136, 521–573 (2012)
14. Fiscella, A., Servadei, R., Valdinoci, E.: Density properties for fractional Sobolev spaces (2014, preprint)
15. Franzina, G., Palatucci, G.: Fractional p-eigenvalues. Riv. Mat. Univ. Parma. 5 (2014)
16. Garcìa Azorero J.P., Peral Alonso I., Manfredi J.J.: Sobolev versus Hölder local minimizers and global multiplicity for some quasilinear elliptic equations. Commun. Contemp. Math. 2, 385–404 (2000)
17. Iannizzotto, A., Liu, S., Perera, K., Squassina, M.: Existence results for fractional p-Laplacian problems via Morse theory (2014, preprint)
18. Li S., Perera K., Su J.: Computation of critical groups in elliptic boundary-value problems where the asymptotic limits may not exist. Proc. R. Soc. Edinburgh Sec. A. 131, 721–732 (2001)
19. Lindgren E., Lindqvist P.: Fractional eigenvalues. Calc. Var. PDE. 49, 795–826 (2014)
20. Liu J., Liu S.: The existence of multiple solutions to quasilinear elliptic equations. Bull. London Math. Soc. 37, 592–600 (2005)
21. Mingione G.: Gradient potential estimates. J. Eur. Math. Soc. 13, 459–486 (2011)
22. 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)
23. Ros-Oton X., Serra J.: The Pohožaev identity for the fractional laplacian. Arch. Rat. Mech. Anal. 213, 587–628 (2014)
24. Ros-Oton, X., Serra, J.: Nonexistence results for nonlocal equations with critical and supercritical nonlinearities. Commun. Partial Differ. Equ. (2014, to appear)
25. Servadei R., Valdinoci E.: Mountain pass solutions for non-local elliptic operators. J. Math. Anal. Appl. 389, 887–898 (2012)
26. Servadei R., Valdinoci E.: Variational methods for non-local operators of elliptic type. Discrete Contin. Dyn. Syst. 33, 2105–2137 (2013)
27. Servadei R., Valdinoci E.: Lewy-Stampacchia type estimates for variational inequalities driven by (non)local operators. Rev. Mat. Iberoam. 29, 1091–1126 (2013)
28. Servadei, R., Valdinoci, E.: The Brezis–Nirenberg result for the fractional Laplacian. Trans. Am. Math. Soc. (2014, to appear)
29. Servadei R., Valdinoci E.: Weak and viscosity solutions of the fractional Laplace equation. Publ. Mat. 58, 1–261 (2014)
30. Silvestre L.: Regularity of the obstacle problem for a fractional power of the laplace operator. Commun. Pure Appl. Math. 60, 67–112 (2007)