Fractional p-eigenvalues

Rivista di Matematica della Universita di Parma

Volumn 5, Issue 2, 2014, Pages 373-386

  Franzina, Giovanni ^a   Palatucci, Giampiero ^b  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

^b UNIVERSITY OF PARMA   (Italy)

Author keywords

Caccioppoli estimates; Dirichlet forms; Fractional laplacian; Nonlinear eigenvalues problems; Nonlocal problem; Quasilinear nonlocal operators

Indexed keywords

EID: 84905012689     PISSN: 00356298     EISSN: 22842578     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. M. BELLONI and B. KAWOHL, A direct uniqueness proof for equations involving the p-Laplace operator, Manuscripta Math. 109(2002), no. 2, 229-231.
2. M. BELLONI and B. KAWOHL, The pseudo-p-Laplace eigenvalue problem and viscosity solutions as p → ∞, ESAIM Control Optim. Calc. Var. 10(2004), no. 1, 28-52.
3. R. BENGURIA, H. BREZIS and E. H. LIEB, The Thomas-Fermi-von Weizsacker theory of atoms and molecules, Comm. Math. Phys. 79(1981), no. 2, 167-180.
4. L. BRASCO and G. FRANZINA, A note on positive eigenfunctions and hidden convexity, Arch. Math. (Basel) 99(2012), no. 4, 367-374.
5. L. CAFFARELLI and L. SILVESTRE, An extension problem related to the fractional Laplacian, Comm. Partial Differential Equations 32(2007), no. 7-9, 1245-1260.
6. A. DI CASTRO, T. KUUSI and G. PALATUCCI, Local behavior of fractional pminimizers, submitted paper.
7. A. DI CASTRO, T. KUUSI and G. PALATUCCI, Nonlocal Harnack inequalities, J. Funct. Anal. 267(2014), no. 6, 1807-1836.
8. A. DI CASTRO and G. PALATUCCI, Fractional regularity for nonlinear elliptic problems with measure data, J. Convex Anal. 20(2013), no. 4, 901-918.
9. E. DI NEZZA, G. PALATUCCI and E. VALDINOCI, Hitchhiker's guide to the fractional Sobolev spaces, Bull. Sci. Math. 136(2012), no. 5, 521-573.
10. G. FRANZINA and E. VALDINOCI, Geometric analysis of fractional phase transition interfaces. Geometric properties for parabolic and elliptic PDE's, Springer INdAM Ser., 2, Springer, Milan 2013, 117-130.
11. M. KASSMANN, A priori estimates for integro-differential operators with measurable kernels, Calc. Var. Partial Differential Equations 34(2009), no. 1, 1-21.
12. O. A. LADYZHENSKAYA and N. N. URAL'TSEVA, Linear and quasilinear elliptic equations, Academic Press, New York-London 1968.
13. E. LINDGREN and P. LINDQVIST, Fractional eigenvalues, Calc. Var. Partial Differential Equations 49(2014), no. 1-2, 795-826.
14. P. LINDQVIST, On the equation div (|∇u|p-2∇u) + λ|u|p-2u = 0, Proc. Amer. Math. Soc. 109(1990), no. 1, 157-164.
15. P. LINDQVIST, Addendum: "On the equation |∇u|p-2∇u) + λ|u|p-2 = 0", Proc. Amer. Math. Soc. 116(1992), no. 2, 583-584.
16. G. MINGIONE, The Calderón-Zygmund theory for elliptic problems with measure data, Ann. Sc. Norm. Super. Pisa CI. Sci. (5) 6(2007), no. 2, 195-261.
17. G. MINGIONE, Gradient potential estimates, J. Eur. Math. Soc. (JEMS) 13(2011), no. 2, 459-486.
18. G. PALATUCCI and A. PISANTE, Improved Sobolev embeddings, profile decomposition, and concentration-compactness for fractional Sobolev spaces, Calc. Var. Partial Differential Equations 50(2014), no. 3-4, 799-829.
19. G. PALATUCCI, A. PISANTE and Y. SIRE, Subcritical approximation of a Yamabe type non local equation: a Gamma-convergence approach, Ann. Sc. Norm. Super. Pisa CI. Sci. (5), DOI: 10.2422/2036-2145.201302-006.
20. G. PALATUCCI, O. SAVIN and E. VALDINOCI, Local and global minimizers for a variational energy involving a fractional norm, Ann. Mat. Pura Appl. (4) 192(2013), no. 4, 673-718.
21. O. SAVIN and E. VALDINOCI, Density estimates for a variational model driven by the Gagliardo norm, J. Math. Pures Appl. (9) 101(2014), no. 1, 1-26.
22. R. SERVADEI and E. VALDINOCI, A Brezis-Nirenberg result for non-local critical equations in low dimension, Commun. Pure Appl. Anal. 12(2013), no. 6, 2445-2464.
23. R. SERVADEI and E. VALDINOCI, Variational methods for non-local operators of elliptic type, Discrete Contin. Dyn. Syst. 33(2013), no. 5, 2105-2137.
24. R. SERVADEI and E. VALDINOCI, Weak and viscosity solutions of the fractional Laplace equation, Publ. Mat. 58(2014), no. 1, 133-154.