메뉴 건너뛰기




Volumn 257, Issue 5, 2014, Pages 1457-1486

Semilinear fractional elliptic equations involving measures

Author keywords

Bessel capacities; Dirac measure; Fractional Laplacian; Green kernel; Radon measure

Indexed keywords


EID: 84902550671     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2014.05.012     Document Type: Article
Times cited : (106)

References (35)
  • 1
    • 0000269824 scopus 로고
    • Singularité séliminables pour des équations semi linéaires
    • Baras P., Pierre M. Singularité séliminables pour des équations semi linéaires. Ann. Inst. Fourier (Grenoble) 1984, 34:185-206.
    • (1984) Ann. Inst. Fourier (Grenoble) , vol.34 , pp. 185-206
    • Baras, P.1    Pierre, M.2
  • 2
    • 0141692156 scopus 로고    scopus 로고
    • Nonlinear problems related to the Thomas-Fermi equation
    • Bénilan Ph., Brezis H. Nonlinear problems related to the Thomas-Fermi equation. J. Evol. Equ. 2003, 3:673-770.
    • (2003) J. Evol. Equ. , vol.3 , pp. 673-770
    • Bénilan, P.1    Brezis, H.2
  • 4
    • 84903821591 scopus 로고    scopus 로고
    • Quasilinear Lane-Emden equations with absorption and measure data
    • in press
    • Bidaut-Véron M.F., Hung N., Véron L. Quasilinear Lane-Emden equations with absorption and measure data. J. Math. Pures Appl. 2014, in press. 10.1016/j.matpur.2013.11.011.
    • (2014) J. Math. Pures Appl.
    • Bidaut-Véron, M.F.1    Hung, N.2    Véron, L.3
  • 5
    • 0034550715 scopus 로고    scopus 로고
    • An elliptic semilinear equation with source term involving boundary measures: the subcritical case
    • Bidaut-Véron M.F., Vivier L. An elliptic semilinear equation with source term involving boundary measures: the subcritical case. Rev. Mat. Iberoam. 2000, 16:477-513.
    • (2000) Rev. Mat. Iberoam. , vol.16 , pp. 477-513
    • Bidaut-Véron, M.F.1    Vivier, L.2
  • 6
    • 0003282411 scopus 로고
    • Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert
    • North-Holland, Amsterdam, Notas de Matematica, vol. 50
    • Brezis H. Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland Math. Stud. 1973, vol. 5. North-Holland, Amsterdam, Notas de Matematica, vol. 50.
    • (1973) North-Holland Math. Stud. , vol.5
    • Brezis, H.1
  • 8
    • 84877327074 scopus 로고    scopus 로고
    • Nonlinear equations for fractional Laplacians I: regularity, maximum principles, and Hamiltonian estimates
    • Non Lineaire, available online 7 February 2013.
    • X. Cabré, Y. Sire, Nonlinear equations for fractional Laplacians I: regularity, maximum principles, and Hamiltonian estimates, Ann. Inst. H. Poincaré Anal. Non Lineaire, available online 7 February 2013.
    • Ann. Inst. H. Poincaré Anal
    • Cabré, X.1    Sire, Y.2
  • 10
    • 68049121967 scopus 로고    scopus 로고
    • Regularity theory for fully non-linear integrodifferential equations
    • Caffarelli L., Silvestre L. Regularity theory for fully non-linear integrodifferential equations. Comm. Pure Appl. Math. 2009, 62:597-638.
    • (2009) Comm. Pure Appl. Math. , vol.62 , pp. 597-638
    • Caffarelli, L.1    Silvestre, L.2
  • 11
    • 0032335134 scopus 로고    scopus 로고
    • Estimates on Green functions and Poisson kernels for symmetric stable process
    • Chen Z., Song R. Estimates on Green functions and Poisson kernels for symmetric stable process. Math. Ann. 1998, 312:465-501.
    • (1998) Math. Ann. , vol.312 , pp. 465-501
    • Chen, Z.1    Song, R.2
  • 14
    • 33644613818 scopus 로고    scopus 로고
    • Classification of solutions for an integral equation
    • Chen W., Li C., Ou B. Classification of solutions for an integral equation. Comm. Pure Appl. Math. 2006, 59:330-343.
    • (2006) Comm. Pure Appl. Math. , vol.59 , pp. 330-343
    • Chen, W.1    Li, C.2    Ou, B.3
  • 16
    • 0010823682 scopus 로고
    • On the integral representation of certain local functionals
    • Dal Maso G. On the integral representation of certain local functionals. Ric. Mat. 1983, 32:85-113.
    • (1983) Ric. Mat. , vol.32 , pp. 85-113
    • Dal Maso, G.1
  • 17
    • 0010467921 scopus 로고
    • Topologies fines et compactifications associées à certains espaces de Dirichlet
    • Feyel D., de la Pradelle A. Topologies fines et compactifications associées à certains espaces de Dirichlet. Ann. Inst. Fourier (Grenoble) 1977, 27:121-146.
    • (1977) Ann. Inst. Fourier (Grenoble) , vol.27 , pp. 121-146
    • Feyel, D.1    de la Pradelle, A.2
  • 18
    • 84974004263 scopus 로고
    • Boundary singularities of solutions of some nonlinear elliptic equations
    • Gmira A., Véron L. Boundary singularities of solutions of some nonlinear elliptic equations. Duke Math. J. 1991, 64:271-324.
    • (1991) Duke Math. J. , vol.64 , pp. 271-324
    • Gmira, A.1    Véron, L.2
  • 19
    • 84869095057 scopus 로고    scopus 로고
    • Existence of minimizers of functionals involving the fractional gradient in the absence of compactness
    • Hajaiej H. Existence of minimizers of functionals involving the fractional gradient in the absence of compactness. J. Math. Anal. Appl. 2013, 399:17-26.
    • (2013) J. Math. Anal. Appl. , vol.399 , pp. 17-26
    • Hajaiej, H.1
  • 21
    • 78951479821 scopus 로고    scopus 로고
    • A duality approach to the fractional Laplacian with measure data
    • Karisen K., Petitta F., Ulusoy S. A duality approach to the fractional Laplacian with measure data. Publ. Mat. 2011, 55:151-161.
    • (2011) Publ. Mat. , vol.55 , pp. 151-161
    • Karisen, K.1    Petitta, F.2    Ulusoy, S.3
  • 22
    • 2442503290 scopus 로고    scopus 로고
    • Remark on some conformally invariant integral equations: the method for moving spheres
    • Li Y.Y. Remark on some conformally invariant integral equations: the method for moving spheres. J. Eur. Math. Soc. (JEMS) 2004, 6:153-180.
    • (2004) J. Eur. Math. Soc. (JEMS) , vol.6 , pp. 153-180
    • Li, Y.Y.1
  • 23
    • 0040249151 scopus 로고    scopus 로고
    • The boundary trace of positive solutions of semilinear elliptic equations: the subcritical case
    • Marcus M., Véron L. The boundary trace of positive solutions of semilinear elliptic equations: the subcritical case. Arch. Ration. Mech. Anal. 1998, 144:201-231.
    • (1998) Arch. Ration. Mech. Anal. , vol.144 , pp. 201-231
    • Marcus, M.1    Véron, L.2
  • 24
    • 0032065325 scopus 로고    scopus 로고
    • The boundary trace of positive solutions of semilinear elliptic equations: the supercritical case
    • Marcus M., Véron L. The boundary trace of positive solutions of semilinear elliptic equations: the supercritical case. J. Math. Pures Appl. 1998, 77:481-524.
    • (1998) J. Math. Pures Appl. , vol.77 , pp. 481-524
    • Marcus, M.1    Véron, L.2
  • 25
    • 0035597042 scopus 로고    scopus 로고
    • Removable singularities and boundary traces
    • Marcus M., Véron L. Removable singularities and boundary traces. J. Math. Pures Appl. 2001, 80:879-900.
    • (2001) J. Math. Pures Appl. , vol.80 , pp. 879-900
    • Marcus, M.1    Véron, L.2
  • 26
    • 2442572116 scopus 로고    scopus 로고
    • The boundary trace and generalized B.V.P. for semilinear elliptic equations with coercive absorption
    • Marcus M., Véron L. The boundary trace and generalized B.V.P. for semilinear elliptic equations with coercive absorption. Comm. Pure Appl. Math. 2003, 56:689-731.
    • (2003) Comm. Pure Appl. Math. , vol.56 , pp. 689-731
    • Marcus, M.1    Véron, L.2
  • 27
    • 84863469913 scopus 로고    scopus 로고
    • Hitchhiker's guide to the fractional Sobolev spaces
    • Di Nezza E., Palatucci G., Valdinoci E. Hitchhiker's guide to the fractional Sobolev spaces. Bull. Sci. Math. 2012, 136:521-573.
    • (2012) Bull. Sci. Math. , vol.136 , pp. 521-573
    • Di Nezza, E.1    Palatucci, G.2    Valdinoci, E.3
  • 28
    • 84894498072 scopus 로고    scopus 로고
    • The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
    • March
    • Ros-Oton X., Serra J. The Dirichlet problem for the fractional Laplacian: regularity up to the boundary. J. Math. Pures Appl. March 2014, 101(3):275-302.
    • (2014) J. Math. Pures Appl. , vol.101 , Issue.3 , pp. 275-302
    • Ros-Oton, X.1    Serra, J.2
  • 29
    • 59849109073 scopus 로고    scopus 로고
    • Fractional Laplacian phase transitions and boundary reactions: a geometric inequality and a symmetry result
    • Sire Y., Valdinoci E. Fractional Laplacian phase transitions and boundary reactions: a geometric inequality and a symmetry result. J. Funct. Anal. 2009, 256:1842-1864.
    • (2009) J. Funct. Anal. , vol.256 , pp. 1842-1864
    • Sire, Y.1    Valdinoci, E.2
  • 30
    • 84980081501 scopus 로고
    • p-estimates for solutions of second order elliptic equations
    • p-estimates for solutions of second order elliptic equations. Comm. Pure Appl. Math. 1963, 16:505-510.
    • (1963) Comm. Pure Appl. Math. , vol.16 , pp. 505-510
    • Stampacchia, G.1
  • 31
    • 51249173684 scopus 로고
    • Sur un lemme d'équivalence utilisé en analyse numérique
    • Tartar L. Sur un lemme d'équivalence utilisé en analyse numérique. Calcolo 1987, 24:129-140.
    • (1987) Calcolo , vol.24 , pp. 129-140
    • Tartar, L.1
  • 33
    • 0000227922 scopus 로고
    • Singular solutions of some nonlinear elliptic equations
    • Véron L. Singular solutions of some nonlinear elliptic equations. Nonlinear Anal. 1981, 5:225-242.
    • (1981) Nonlinear Anal. , vol.5 , pp. 225-242
    • Véron, L.1
  • 34
    • 33847723977 scopus 로고    scopus 로고
    • Elliptic equations involving measures
    • North-Holland, Amsterdam, Stationary Partial Differential Equations, vol. I
    • Véron L. Elliptic equations involving measures. Handb. Differ. Equ. 2004, 593-712. North-Holland, Amsterdam.
    • (2004) Handb. Differ. Equ. , pp. 593-712
    • Véron, L.1
  • 35
    • 84884653188 scopus 로고    scopus 로고
    • Existence and stability of solutions of general semilinear elliptic equations with measure data
    • Véron L. Existence and stability of solutions of general semilinear elliptic equations with measure data. Adv. Nonlinear Stud. 2013, 13:447-460.
    • (2013) Adv. Nonlinear Stud. , vol.13 , pp. 447-460
    • Véron, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.