메뉴 건너뛰기




Volumn 6, Issue 2, 2007, Pages 335-366

Eigenvalue, maximum principle and regularity for fully non linear homogeneous operators

Author keywords

Eigenvalue; Fully nonlinear equation; Viscosity solution

Indexed keywords


EID: 34248214768     PISSN: 15340392     EISSN: 15535258     Source Type: Journal    
DOI: 10.3934/cpaa.2007.6.335     Document Type: Article
Times cited : (106)

References (27)
  • 1
    • 0000623205 scopus 로고
    • Simplicité et isolation de la première valeur propre du p-laplacien avec poids
    • A. Anane, Simplicité et isolation de la première valeur propre du p-laplacien avec poids, C. R. Acad. Sci. Paris Sr. I Math., 305 (1987), no. 16, 725-728.
    • (1987) C. R. Acad. Sci. Paris Sr. I Math , vol.305 , Issue.16 , pp. 725-728
    • Anane, A.1
  • 2
    • 0033247049 scopus 로고    scopus 로고
    • On the strong maximum principle for fully nonlinear degenerate elliptic equations
    • M. Bardi and F. Da Lio, On the strong maximum principle for fully nonlinear degenerate elliptic equations, Archiv. Math, n., 73 (1999), 276-285.
    • (1999) Archiv. Math , Issue.and 73 , pp. 276-285
    • Bardi, M.1    Da Lio, F.2
  • 3
    • 84990602584 scopus 로고
    • The principal eigenvalue and maximum principle for second-order elliptic operators in general domains
    • H. Berestycki, L. Nirenberg and S.R.S. Varadhan, The principal eigenvalue and maximum principle for second-order elliptic operators in general domains, Comm. Pure Appl. Math., 47 (1994), no. 1, 47-92.
    • (1994) Comm. Pure Appl. Math , vol.47 , Issue.1 , pp. 47-92
    • Berestycki, H.1    Nirenberg, L.2    Varadhan, S.R.S.3
  • 4
    • 34248157803 scopus 로고    scopus 로고
    • I. Birindelli and F. Demengel, Comparison principle and Liouville type results for singular fully nonlinear operators, Ann. Fac. Sci Toulouse Math, 13 (2004), no.6, N.2, 261-287.
    • I. Birindelli and F. Demengel, Comparison principle and Liouville type results for singular fully nonlinear operators, Ann. Fac. Sci Toulouse Math, 13 (2004), no.6, N.2, 261-287.
  • 5
    • 34247141781 scopus 로고    scopus 로고
    • Eigenvalue and Maximum principle for fully nonlinear singular operators, Advances in Partial Diff
    • I. Birindelli and F. Demengel, Eigenvalue and Maximum principle for fully nonlinear singular operators, Advances in Partial Diff. Equations, 11(2006), no. 1, 91-119.
    • (2006) Equations , vol.11 , Issue.1 , pp. 91-119
    • Birindelli, I.1    Demengel, F.2
  • 8
    • 13844322232 scopus 로고    scopus 로고
    • Nonlinear eigenvalues and bifurcation problems for Pucci's operator, Annales de l'Institut H
    • J. Busca, M.J. Esteban and A. Quaas, Nonlinear eigenvalues and bifurcation problems for Pucci's operator, Annales de l'Institut H. Poincaré, Analyse non-linéaire, 22 (2005), 187-206.
    • (2005) Poincaré, Analyse non-linéaire , vol.22 , pp. 187-206
    • Busca, J.1    Esteban, M.J.2    Quaas, A.3
  • 10
    • 84972499852 scopus 로고
    • Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
    • Y.G. Chen, Y. Giga and S. Goto, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, J. Differential Geom-, 33 (1991), no. 3, 749-786.
    • (1991) J. Differential Geom , vol.33 , Issue.3 , pp. 749-786
    • Chen, Y.G.1    Giga, Y.2    Goto, S.3
  • 11
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • M.G. Crandall, H. Ishii and P.L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.), 27 (1992), no. 1, 1-67.
    • (1992) Bull. Amer. Math. Soc. (N.S.) , vol.27 , Issue.1 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.L.3
  • 12
    • 0038173085 scopus 로고    scopus 로고
    • On the Liouville property for fully-nonlinear equations Annales de l'Institut H
    • A. Cutri and F. Leoni, On the Liouville property for fully-nonlinear equations Annales de l'Institut H. Poincaré, Analyse non-linéaire, 17 (2000), 219-245.
    • (2000) Poincaré, Analyse non-linéaire , vol.17 , pp. 219-245
    • Cutri, A.1    Leoni, F.2
  • 13
    • 84968469617 scopus 로고
    • Curvature measures
    • H. Federer, Curvature measures, Trans. Amer. Math. Soc., 93 (1959), 418-491.
    • (1959) Trans. Amer. Math. Soc , vol.93 , pp. 418-491
    • Federer, H.1
  • 14
    • 84968513647 scopus 로고
    • Regularity of the distance function
    • R.L. Foote, Regularity of the distance function, Proc. Amer. Math. Soc., 92 (1984), no. 1, 153-155.
    • (1984) Proc. Amer. Math. Soc , vol.92 , Issue.1 , pp. 153-155
    • Foote, R.L.1
  • 16
    • 0346878612 scopus 로고    scopus 로고
    • Viscosity solutions of non-linear partial differential equations
    • H. Ishii, Viscosity solutions of non-linear partial differential equations Sugaku Expositions, 9 (1996), 135-152.
    • (1996) Sugaku Expositions , vol.9 , pp. 135-152
    • Ishii, H.1
  • 17
    • 0002824461 scopus 로고
    • Viscosity solutions of Fully- Nonlinear Second Order Elliptic Partial Differential Equations
    • H. Ishii and P.L. Lions, Viscosity solutions of Fully- Nonlinear Second Order Elliptic Partial Differential Equations, J. Differential Equations, 83 (1990), no. 1, 26-78.
    • (1990) J. Differential Equations , vol.83 , Issue.1 , pp. 26-78
    • Ishii, H.1    Lions, P.L.2
  • 19
    • 0036345277 scopus 로고    scopus 로고
    • On the equivalence o f viscosity solutions and weak solutions for a quasi linear equation
    • P. Juutinen, P. Lindqvist and J. Manfredi, On the equivalence o f viscosity solutions and weak solutions for a quasi linear equation, SIAM J. Math. Anal., 33 (2001), no. 3, 699-717.
    • (2001) SIAM J. Math. Anal , vol.33 , Issue.3 , pp. 699-717
    • Juutinen, P.1    Lindqvist, P.2    Manfredi, J.3
  • 22
    • 34248178647 scopus 로고    scopus 로고
    • P. Lindqvist, On a nonlinear eigenvalue problem, Fall School in Analysis (Jyvskyl, 1994), Report, 68, Univ. Jyvskyl, Jyvskyl, (1995), 33-54.
    • P. Lindqvist, On a nonlinear eigenvalue problem, Fall School in Analysis (Jyvskyl, 1994), Report, 68, Univ. Jyvskyl, Jyvskyl, (1995), 33-54.
  • 23
    • 0020703936 scopus 로고
    • Bifurcation and optimal stochastic control
    • P.L. Lions, Bifurcation and optimal stochastic control, Nonlinear Anal., 7 (1983), no. 2, 177-207.
    • (1983) Nonlinear Anal , vol.7 , Issue.2 , pp. 177-207
    • Lions, P.L.1
  • 25
    • 13844311974 scopus 로고    scopus 로고
    • Existence of positive solutions to a "semilinear" equation involving the Pucci's operators in a convex domain
    • A. Quaas, Existence of positive solutions to a "semilinear" equation involving the Pucci's operators in a convex domain, Differential Integral Equations, 17 (2004), no. 5-6, 481-494.
    • (2004) Differential Integral Equations , vol.17 , Issue.5-6 , pp. 481-494
    • Quaas, A.1
  • 26
    • 29944433225 scopus 로고    scopus 로고
    • On the principal eigenvalues and the Dirichlet problem for fully nonlinear operators
    • A. Quaas and B. Sirakov, On the principal eigenvalues and the Dirichlet problem for fully nonlinear operators, C. R. Math. Acad. Sci. Paris, 342 (2006), no. 2, 115-118.
    • (2006) C. R. Math. Acad. Sci. Paris , vol.342 , Issue.2 , pp. 115-118
    • Quaas, A.1    Sirakov, B.2
  • 27
    • 0001335714 scopus 로고
    • A strong maximum principle for some quasilinear elliptic equations
    • J.L. Vazquez, A strong maximum principle for some quasilinear elliptic equations, Appl. Math. Optim., 12 (1984), no. 3, 191-202.
    • (1984) Appl. Math. Optim , vol.12 , Issue.3 , pp. 191-202
    • Vazquez, J.L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.