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Volumn 36, Issue 4, 2016, Pages 1813-1845

Stability of variational eigenvalues for the fractional p-Laplacian

Author keywords

Critical points; Fractional p Laplacian; Nonlocal eigenvalue problems; convergence

Indexed keywords


EID: 84943525413     PISSN: 10780947     EISSN: 15535231     Source Type: Journal    
DOI: 10.3934/dcds.2016.36.1813     Document Type: Article
Times cited : (152)

References (38)
  • 2
    • 27844463496 scopus 로고    scopus 로고
    • Lévy processes - From probability to finance and quantum groups
    • D. Applebaum, Lévy processes - from probability to finance and quantum groups, Notices Amer. Math. Soc., 51 (2004), 1336-1347.
    • (2004) Notices Amer. Math. Soc. , vol.51 , pp. 1336-1347
    • Applebaum, D.1
  • 7
    • 85032142769 scopus 로고    scopus 로고
    • The second eigenvalue of the fractional p-Laplacian
    • to appear on
    • L. Brasco and E. Parini, The second eigenvalue of the fractional p-Laplacian, to appear on Adv. Calc. Var. (2015)
    • (2015) Adv. Calc. Var.
    • Brasco, L.1    Parini, E.2
  • 8
    • 84894039977 scopus 로고    scopus 로고
    • Nonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates
    • X. Cabré and Y. Sire, Nonlinear equations for fractional Laplacians, I: Regularity, maximum principles, and Hamiltonian estimates, Ann. Inst. H. Poincaré Anal. Non Linéaire, 31 (2014), 23-53.
    • (2014) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.31 , pp. 23-53
    • Cabré, X.1    Sire, Y.2
  • 9
    • 84867962044 scopus 로고    scopus 로고
    • Nonlocal equations, drifts and games, Nonlinear partial differential equations
    • L. A. Caffarelli, Nonlocal equations, drifts and games, Nonlinear partial differential equations, Abel Symposia, 7 (2012), 37-52.
    • (2012) Abel Symposia , vol.7 , pp. 37-52
    • Caffarelli, L.A.1
  • 10
    • 38549181235 scopus 로고    scopus 로고
    • Asymptotic behaviour of nonlinear eigenvalue problems involving p-Laplacian-type operators
    • T. Champion and L. De Pascale, Asymptotic behaviour of nonlinear eigenvalue problems involving p-Laplacian-type operators, Proc. Roy. Soc. Edinburgh Sect. A, 137 (2007), 1179-1195.
    • (2007) Proc. Roy. Soc. Edinburgh Sect. A , vol.137 , pp. 1179-1195
    • Champion, T.1    De Pascale, L.2
  • 15
    • 10244239422 scopus 로고    scopus 로고
    • A fractional order Hardy inequality
    • B. Dyda, A fractional order Hardy inequality, Illinois J. Math., 48 (2004), 575-588.
    • (2004) Illinois J. Math. , vol.48 , pp. 575-588
    • Dyda, B.1
  • 16
    • 0003346795 scopus 로고
    • Measure theory and fine properties of functions
    • CRC Press, Boca Raton, FL
    • L. C. Evans and R. F. Gariepy, Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics. CRC Press, Boca Raton, FL, 1992.
    • (1992) Studies in Advanced Mathematics
    • Evans, L.C.1    Gariepy, R.F.2
  • 17
    • 0001959537 scopus 로고
    • Bifurcation for odd potential operators and an alternative topological index
    • E. R. Fadell and P. H. Rabinowitz, Bifurcation for odd potential operators and an alternative topological index, J. Funct. Anal., 26 (1977), 48-67.
    • (1977) J. Funct. Anal. , vol.26 , pp. 48-67
    • Fadell, E.R.1    Rabinowitz, P.H.2
  • 19
    • 65049088386 scopus 로고    scopus 로고
    • Springer Monographs in Mathematics. Springer, New York
    • p Spaces, Springer Monographs in Mathematics. Springer, New York, 2007.
    • (2007) p Spaces
    • Fonseca, I.1    Leoni, G.2
  • 24
    • 21944446696 scopus 로고    scopus 로고
    • On the eigenvalue of the p-Laplacian with varying p
    • Y. X. Huang, On the eigenvalue of the p-Laplacian with varying p, Proc. Amer. Math. Soc., 125 (1997), 3347-3354.
    • (1997) Proc. Amer. Math. Soc. , vol.125 , pp. 3347-3354
    • Huang, Y.X.1
  • 25
    • 84939181654 scopus 로고    scopus 로고
    • Existence results for fractional P-laplacian problems via Morse theory
    • to appear on
    • A. Iannizzotto, S. Liu, K. Perera and M. Squassina, Existence results for fractional p-Laplacian problems via Morse theory, to appear on Adv. Calc. Var., (2015)
    • (2015) Adv. Calc. Var.
    • Iannizzotto, A.1    Liu, S.2    Perera, K.3    Squassina, M.4
  • 26
    • 85006953017 scopus 로고    scopus 로고
    • Global Hölder regularity for the fractional p-Laplacian
    • arXiv:1411.2956
    • A. Iannizzotto, S. Mosconi and M. Squassina, Global Hölder regularity for the fractional p-Laplacian, to appear on Rev. Mat. Iberoam., available at arXiv:1411.2956
    • Rev. Mat. Iberoam.
    • Iannizzotto, A.1    Mosconi, S.2    Squassina, M.3
  • 27
    • 84905034992 scopus 로고    scopus 로고
    • Weyl-type laws for fractional p-eigenvalue problems
    • A. Iannizzotto and M. Squassina, Weyl-type laws for fractional p-eigenvalue problems, Asymptot. Anal., 88 (2014), 233-245.
    • (2014) Asymptot. Anal. , vol.88 , pp. 233-245
    • Iannizzotto, A.1    Squassina, M.2
  • 28
    • 84928738414 scopus 로고    scopus 로고
    • Nonlocal equations with measure data
    • T. Kuusi, G. Mingione and Y. Sire, Nonlocal equations with measure data, Comm. Math. Phys., 337 (2015), 1317-1368.
    • (2015) Comm. Math. Phys. , vol.337 , pp. 1317-1368
    • Kuusi, T.1    Mingione, G.2    Sire, Y.3
  • 29
    • 84929758705 scopus 로고    scopus 로고
    • Nonlocal self-improving properties
    • T. Kuusi, G. Mingione and Y. Sire, Nonlocal self-improving properties, Anal. PDE, 8 (2015), 57-114.
    • (2015) Anal. PDE , vol.8 , pp. 57-114
    • Kuusi, T.1    Mingione, G.2    Sire, Y.3
  • 31
    • 0040043873 scopus 로고
    • On non-linear Rayleigh quotients
    • P. Lindqvist, On non-linear Rayleigh quotients, Potential Anal., 2 (1993), 199-218.
    • (1993) Potential Anal. , vol.2 , pp. 199-218
    • Lindqvist, P.1
  • 32
    • 84891902305 scopus 로고    scopus 로고
    • Convergence of the eigenvalues of the p-Laplace operator as p goes to 1
    • S. Littig and F. Schuricht, Convergence of the eigenvalues of the p-Laplace operator as p goes to 1, Calc. Var. Partial Differential Equations, 49 (2014), 707-727.
    • (2014) Calc. Var. Partial Differential Equations , vol.49 , pp. 707-727
    • Littig, S.1    Schuricht, F.2
  • 33
    • 77954142411 scopus 로고    scopus 로고
    • Hardy inequalities for fractional integrals on general domains
    • M. Loss and C. Sloane, Hardy inequalities for fractional integrals on general domains, J. Funct. Anal., 259 (2010), 1369-1379.
    • (2010) J. Funct. Anal. , vol.259 , pp. 1369-1379
    • Loss, M.1    Sloane, C.2
  • 34
    • 0037058485 scopus 로고    scopus 로고
    • On the Bourgain, Brezis, and Mironescu theorem concerning limiting embeddings of fractional Sobolev spaces
    • V. Maz'ya and T. Shaposhnikova, On the Bourgain, Brezis, and Mironescu theorem concerning limiting embeddings of fractional Sobolev spaces, J. Funct. Anal., 195 (2002), 230-238.
    • (2002) J. Funct. Anal. , vol.195 , pp. 230-238
    • Maz'Ya, V.1    Shaposhnikova, T.2
  • 35
    • 79956128505 scopus 로고    scopus 로고
    • Continuity of the variational eigenvalues of the p-Laplacian with respect to p
    • E. Parini, Continuity of the variational eigenvalues of the p-Laplacian with respect to p, Bull. Aust. Math. Soc., 83 (2011), 376-381.
    • (2011) Bull. Aust. Math. Soc. , vol.83 , pp. 376-381
    • Parini, E.1
  • 36
    • 1142288658 scopus 로고    scopus 로고
    • A new approach to Sobolev spaces and connections to Γ-convergence
    • A. Ponce, A new approach to Sobolev spaces and connections to Γ-convergence, Calc. Var. Partial Differential Equations, 19 (2004), 229-255.
    • (2004) Calc. Var. Partial Differential Equations , vol.19 , pp. 229-255
    • Ponce, A.1
  • 37
    • 70449581236 scopus 로고    scopus 로고
    • Rigidity results for some boundary quasilinear phase transitions
    • Y. Sire and E. Valdinoci, Rigidity results for some boundary quasilinear phase transitions, Commun. Partial Differ. Equations, 34 (2009), 765-784.
    • (2009) Commun. Partial Differ. Equations , vol.34 , pp. 765-784
    • Sire, Y.1    Valdinoci, E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.