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Volumn 58, Issue 1, 2014, Pages 133-154

Weak and viscosity solutions of the fractional laplace equation

Author keywords

Fractional laplacian; Integrodifferential operators; Regularity theory.; Viscosity solutions; Weak solutions

Indexed keywords


EID: 84987763937     PISSN: 02141493     EISSN: 20144350     Source Type: Journal    
DOI: 10.5565/PUBLMAT_58114_08     Document Type: Article
Times cited : (7)

References (15)
  • 1
    • 42549114402 scopus 로고    scopus 로고
    • On the Dirichlet problem for second-order elliptic integro-differential equations
    • G. Barles, 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. DOI: 10.1512/iumj. 2008.57.3315.
    • (2008) Indiana Univ. Math. J. , vol.57 , Issue.1 , pp. 213-246
    • Barles, G.1    Chasseigne, E.2    Imbert, C.3
  • 2
    • 84930245811 scopus 로고    scopus 로고
    • Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces
    • appear
    • B. Barrios Barrera, A. Figalli, and E. Valdinoci, Bootstrap regularity for integro-differential operators and its application to nonlocal minimal surfaces, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) (to appear). DOI: 10.2422/2036-2145.201202 -007.
    • Ann. Sc. Norm. Super. Pisa Cl. Sci , vol.5
    • Barrera, B.B.1    Figalli, A.2    Valdinoci, E.3
  • 3
    • 34548348805 scopus 로고    scopus 로고
    • An extension problem related to the fractional Laplacian
    • L. Caffarelli and L. Silvestre, An extension problem related to the fractional Laplacian, Comm. Partial Differential Equations 32(7-9) (2007), 1245-1260. DOI: 10.1080/03605300600987306.
    • (2007) Comm. Partial Differential Equations , vol.32 , Issue.7-9 , pp. 1245-1260
    • Caffarelli, L.1    Silvestre, L.2
  • 4
    • 68049121967 scopus 로고    scopus 로고
    • Regularity theory for fully nonlinear integro-differential equations
    • L. Caffarelli and L. Silvestre, Regularity theory for fully nonlinear integro-differential equations, Comm. Pure Appl. Math. 62(5) (2009), 597-638. DOI: 10.1002/cpa.20274.
    • (2009) Comm. Pure Appl. Math. , vol.62 , Issue.5 , pp. 597-638
    • Caffarelli, L.1    Silvestre, L.2
  • 5
    • 79952706153 scopus 로고    scopus 로고
    • Regularity results for nonlocal equations by approximation
    • L. Caffarelli and L. Silvestre, Regularity results for nonlocal equations by approximation, Arch. Ration. Mech. Anal. 200(1) (2011), 59-88. DOI: 10.1007/s00205-010-0336-4.
    • (2011) Arch. Ration. Mech. Anal. , vol.200 , Issue.1 , pp. 59-88
    • Caffarelli, L.1    Silvestre, L.2
  • 6
    • 84863469913 scopus 로고    scopus 로고
    • Hitchhiker's guide to the fractional Sobolev spaces
    • E. Di Nezza, G. Palatucci, and E. Valdinoci, Hitchhiker's guide to the fractional Sobolev spaces, Bull. Sci. Math. 136(5) (2012), 521-573. DOI: 10.1016/j.bulsci.2011.12.004.
    • (2012) Bull. Sci. Math. , vol.136 , Issue.5 , pp. 521-573
    • Nezza, E.D.1    Palatucci, G.2    Valdinoci, E.3
  • 7
    • 84155167485 scopus 로고    scopus 로고
    • On Lp -estimates for a class of non-local elliptic equations
    • H. Dong and D. Kim, On Lp -estimates for a class of non-local elliptic equations, J. Funct. Anal. 262(3) (2012), 1166-1199. DOI: 10.1016/j.jfa.2011.11.002.
    • (2012) J. Funct. Anal. , vol.262 , Issue.3 , pp. 1166-1199
    • Dong, H.1    Kim, D.2
  • 9
    • 0003643984 scopus 로고
    • Translated from the Russian by A. P. Doohovskoy, Die Grundlehren der mathematischen Wissenschaften 180, Springer-Verlag, New York-Heidelberg
    • N. S. Landkof, "Foundations of modern potential theory", Translated from the Russian by A. P. Doohovskoy, Die Grundlehren der mathematischen Wissenschaften 180, Springer-Verlag, New York-Heidelberg, 1972.
    • (1972) Foundations of Modern Potential Theory
    • Landkof, N.S.1
  • 10
    • 84862308028 scopus 로고    scopus 로고
    • Fractional Laplacian: Pohozaev identity and nonexistence results
    • Paris
    • X. Ros-Oton and J. Serra, Fractional Laplacian: Pohozaev identity and nonexistence results, C. R. Math. Acad. Sci. Paris 350(9-10) (2012), 505-508. DOI: 10.1016/j.crma.2012.05.011.
    • (2012) C. R. Math. Acad. Sci. , vol.350 , Issue.9-10 , pp. 505-508
    • Ros-Oton, X.1    Serra, J.2
  • 12
    • 84856270145 scopus 로고    scopus 로고
    • Mountain pass solutions for non-local elliptic operators
    • R. Servadei and E. Valdinoci, Mountain pass solutions for non-local elliptic operators, J. Math. Anal. Appl. 389(2) (2012), 887-898. DOI: 10.1016/j.jmaa.2011.12.032.
    • (2012) J. Math. Anal. Appl. , vol.389 , Issue.2 , pp. 887-898
    • Servadei, R.1    Valdinoci, E.2
  • 13
    • 84872157074 scopus 로고    scopus 로고
    • Variational methods for nonlocal operators of elliptic type
    • R. Servadei and E. Valdinoci, Variational methods for nonlocal operators of elliptic type, Discrete Contin. Dyn. Syst. 33(5) (2013), 2105-2137. DOI: 10.3934/dcds.2013.33.2105.
    • (2013) Discrete Contin. Dyn. Syst. , vol.33 , Issue.5 , pp. 2105-2137
    • Servadei, R.1    Valdinoci, E.2
  • 14
    • 84878285487 scopus 로고    scopus 로고
    • A Brezis-Nirenberg result for non-local critical equations in low dimension
    • R. Servadei and E. Valdinoci, A Brezis-Nirenberg result for non-local critical equations in low dimension, Commun. Pure Appl. Anal. 12(6) (2013), 2445-2464. DOI: 10.3934/cpaa.2013.12.2445.
    • (2013) Commun. Pure Appl. Ana.l , vol.12 , Issue.6 , pp. 2445-2464
    • Servadei, R.1    Valdinoci, E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.