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Volumn 42, Issue 3, 2010, Pages 997-1024

Resonance phenomena for second-order stochastic control equations

Author keywords

Bellman operator; Dirichlet problem; Principal eigenvalue; Resonance

Indexed keywords

DIRICHLET PROBLEM; HAMILTON-JACOBI-BELLMAN; PRINCIPAL EIGENVALUES; PROPERTIES OF SOLUTIONS; RESONANCE PHENOMENA; SECOND ORDERS; STOCHASTIC CONTROL; UNIFORMLY ELLIPTIC;

EID: 77953527915     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/080744268     Document Type: Article
Times cited : (13)

References (32)
  • 1
    • 60349114337 scopus 로고    scopus 로고
    • Principal eigenvalues and an anti-maximum principle for nonlinear elliptic equations
    • S. ARMSTRONG, Principal eigenvalues and an anti-maximum principle for nonlinear elliptic equations, J. Differential Equations, 246 (2009), pp. 2958-2987.
    • (2009) J. Differential Equations , vol.246 , pp. 2958-2987
    • Armstrong, S.1
  • 2
    • 67349245863 scopus 로고    scopus 로고
    • The dirichlet problem for the Bellman equation at resonance
    • S. ARMSTRONG, The Dirichlet problem for the Bellman equation at resonance, J. Differential Equations, 247 (2009), pp. 931-955.
    • (2009) J. Differential Equations , vol.247 , pp. 931-955
    • Armstrong, S.1
  • 3
    • 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, Arch. Math. (Basel), 73 (1999), pp. 276-285.
    • (1999) Arch. Math. (Basel) , vol.73 , pp. 276-285
    • Bardi, M.1    Lio, F.D.A.2
  • 4
    • 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), pp. 47-92.
    • (1994) Comm. Pure Appl. Math. , vol.47 , pp. 47-92
    • Berestycki, H.1    Nirenberg, L.2    Varadhan, S.R.S.3
  • 5
    • 34247141781 scopus 로고    scopus 로고
    • First eigenvalue and maximum principle for fully nonlinear singular operators
    • I. BIRINDELLI AND F. DEMENGEL, First eigenvalue and maximum principle for fully nonlinear singular operators, Adv. Differential Equations, 11 (2006), pp. 91-119.
    • (2006) Adv. Differential Equations , vol.11 , pp. 91-119
    • Birindelli, I.1    Demengel, F.2
  • 6
    • 34248214768 scopus 로고    scopus 로고
    • Eigenvalue, maximum principle and regularity for fully non linear homogeneous operators
    • I. BIRINDELLI AND F. DEMENGEL, Eigenvalue, maximum principle and regularity for fully non linear homogeneous operators, Commun. Pure Appl. Anal., 6 (2007), pp. 335-366.
    • (2007) Commun. Pure Appl. Anal. , vol.6 , pp. 335-366
    • Birindelli, I.1    Demengel, F.2
  • 8
    • 4344560340 scopus 로고    scopus 로고
    • Harnack type estimates for nonlinear elliptic systems and applications
    • J. BUSCA AND B. SIRAKOV, Harnack type estimates for nonlinear elliptic systems and applications, Ann. Inst. H. Poincaré, Anal. Non Linéaire, 21 (2004), pp. 543-590.
    • (2004) Ann. Inst. H. Poincaré, Anal. Non Linéaire , vol.21 , pp. 543-590
    • Busca, J.1    Sirakov, B.2
  • 9
    • 44249092576 scopus 로고    scopus 로고
    • Elliptic PDEs in probability and geometry
    • X. CABRÉ, Elliptic PDEs in probability and geometry, Discrete Contin. Dyn. Syst., 20 (2008), pp. 425-457.
    • (2008) Discrete Contin. Dyn. Syst. , vol.20 , pp. 425-457
    • Cabré, X.1
  • 11
    • 0000898166 scopus 로고
    • Interior a priori estimates for solutions of fully non-linear equations
    • L. A. CAFFARELLI, Interior a priori estimates for solutions of fully non-linear equations, Ann. Math., 130 (1989), pp. 189-213.
    • (1989) Ann. Math. , vol.130 , pp. 189-213
    • Caffarelli, L.A.1
  • 12
    • 0040059911 scopus 로고    scopus 로고
    • On Viscosity Solutions of Fully Nonlinear Equations with Measurable Ingredients
    • DOI 10.1002/(SICI)1097-0312(199604)49:4<365::AID-CPA3>3.0.CO;2-A
    • L. CAFFARELLI, M. CRANDALL, M. KOCAN, AND A. SWIECH, On viscosity solutions of fully nonlinear equations with measurable ingredients, Comm. Pure Appl. Math., 49 (1996), pp. 365-398. (Pubitemid 126062481)
    • (1996) Communications on Pure and Applied Mathematics , vol.49 , Issue.4 , pp. 365-398
    • Caffarelli, L.1    Crandall, M.G.2    Kocan, M.3    Swiech, I.4
  • 13
    • 67650880937 scopus 로고    scopus 로고
    • Methods in nonlinear analysis
    • Springer, Berlin
    • K. C. CHANG, Methods in Nonlinear Analysis, Springer Monogr. Math., Springer, Berlin, 2005.
    • (2005) Springer Monogr. Math.
    • Chang, K.C.1
  • 14
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • M. 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), pp. 1-67.
    • (1992) Bull. Amer. Math. Soc. (N. S.) , vol.27 , pp. 1-67
    • Crandall, M.1    Ishii, H.2    Lions, P.L.3
  • 15
    • 84990553687 scopus 로고
    • Classical solutions of fully nonlinear, convex, second-order elliptic equations
    • L. C. EVANS, Classical solutions of fully nonlinear, convex, second-order elliptic equations, Comm. Pure Appl. Math., 25 (1982), pp. 333-363.
    • (1982) Comm. Pure Appl. Math. , vol.25 , pp. 333-363
    • Evans, L.C.1
  • 16
    • 84967792520 scopus 로고
    • Classical solutions of the Hamilton-Jacobi-Bellman equation for uniformly elliptic operators
    • L. C. EVANS, Classical solutions of the Hamilton-Jacobi-Bellman equation for uniformly elliptic operators, Trans. Amer. Math. Soc. 275 (1983), pp. 245-255.
    • (1983) Trans. Amer. Math. Soc. , vol.275 , pp. 245-255
    • Evans, L.C.1
  • 19
    • 33646945027 scopus 로고
    • The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations
    • B. JENSEN, The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations, Arch. Ration. Mech. Anal., 101 (1988), pp. 1-27.
    • (1988) Arch. Ration. Mech. Anal. , vol.101 , pp. 1-27
    • Jensen, B.1
  • 20
    • 0007384467 scopus 로고    scopus 로고
    • Nonlinear second order elliptic equations: Recent development
    • N. V. KRYLOV, FULLY nonlinear second order elliptic equations: Recent development, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 25 (1997), pp. 569-595.
    • (1997) Ann. Sc. Norm. Super. Pisa Cl. Sci. , vol.25 , Issue.5 , pp. 569-595
    • Krylov, N.V.F.1
  • 21
    • 0020703936 scopus 로고
    • Bifurcation and optimal stochastic control
    • P. L. LIONS, Bifurcation and optimal stochastic control, Nonlinear Anal., 7 (1983), pp. 177-207.
    • (1983) Nonlinear Anal. , vol.7 , pp. 177-207
    • Lions, P.L.1
  • 22
    • 0009327760 scopus 로고
    • Résolution analytique des problémes de Bellman-Dirichlet
    • P. L. LIONS, Résolution analytique des problémes de Bellman-Dirichlet, Acta Math., 146 (1981), pp. 151-166.
    • (1981) Acta Math. , vol.146 , pp. 151-166
    • Lions, P.L.1
  • 23
    • 0040450749 scopus 로고
    • Maximum and minimum first eigenvalue for a class of elliptic operators
    • C. PUCCI, Maximum and minimum first eigenvalue for a class of elliptic operators, Proc. Amer. Math. Soc., 17 (1966), pp. 788-795.
    • (1966) Proc. Amer. Math. Soc. , vol.17 , pp. 788-795
    • Pucci, C.1
  • 24
    • 40849137924 scopus 로고    scopus 로고
    • Principal eigenvalues and the dirichlet poblem for fully nonlinear elliptic operators
    • A. QUAAS AND B. SIRAKOV, Principal eigenvalues and the Dirichlet poblem for fully nonlinear elliptic operators, Adv. Math., 218 (2008), pp. 105-135.
    • (2008) Adv. Math. , vol.218 , pp. 105-135
    • Quaas, A.1    Sirakov, B.2
  • 25
    • 67249134379 scopus 로고    scopus 로고
    • Existence and non-existence results for fully nonlinear elliptic systems
    • A. QUAAS AND B. SIRAKOV, Existence and non-existence results for fully nonlinear elliptic systems, Indiana Univ. Math. J., 58 (2009), pp. 751-788.
    • (2009) Indiana Univ. Math. J. , vol.58 , pp. 751-788
    • Quaas, A.1    Sirakov, B.2
  • 26
    • 0041384227 scopus 로고
    • Théorie du degré topologique et applications á des problèmes aux limites nonlinéaires
    • Universite de Paris VI, Paris
    • P. RABINOWITZ, Théorie du degré topologique et applications á des problèmes aux limites nonlinéaires, Publications du Laboratoire d'Analyse Numerique, Universite de Paris VI, Paris, 1975.
    • (1975) Publications du Laboratoire D'Analyse Numerique
    • Rabinowitz, P.1
  • 27
    • 77953531632 scopus 로고    scopus 로고
    • Non uniqueness for the dirichlet problem for fully nonlinear elliptic operators and the ambrosetti-prodi phenomenon
    • B. SIRAKOV, Non Uniqueness for the Dirichlet Problem for Fully Nonlinear Elliptic Operators and the Ambrosetti-Prodi Phenomenon, preprint, 2009, http://hal.archivesouvertes.fr/aut/b oyan+sirakov.
    • (2009) Preprint
    • Sirakov, B.1
  • 28
    • 0000123907 scopus 로고
    • Some remarks on the number of solutions of some nonlinear elliptic problems
    • S. SOLIMINI, Some remarks on the number of solutions of some nonlinear elliptic problems, Ann. Inst. H. Poincaré Anal. Non Linéaire, 2 (1985), pp. 143-156.
    • (1985) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.2 , pp. 143-156
    • Solimini, S.1
  • 30
    • 0003282543 scopus 로고    scopus 로고
    • 1,p-estimates for solutions of fully nonlinear uniformly elliptic equations
    • 1,p-estimates for solutions of fully nonlinear uniformly elliptic equations, Adv. Differential Equations, 2 (1997), pp. 1005-1027.
    • (1997) Adv. Differential Equations , vol.2 , pp. 1005-1027
    • Swiech, A.1
  • 31
    • 84990616983 scopus 로고
    • On the regularity theory of fully nonlinear parabolic equations
    • L. WANG, On the regularity theory of fully nonlinear parabolic equations: I, Comm. Pure Appl. Math., 45 (1992), pp. 27-76.
    • (1992) I, Comm. Pure Appl. Math. , vol.45 , pp. 27-76
    • Wang, L.1
  • 32
    • 67349193998 scopus 로고    scopus 로고
    • 1,p-estimates at the boundary for solutions of fully nonlinear, uniformly elliptic equations
    • 1,p-estimates at the boundary for solutions of fully nonlinear, uniformly elliptic equations, Z. Anal. Adwend. 28 (2009), pp. 129-164.
    • (2009) Z. Anal. Adwend , vol.28 , pp. 129-164
    • Winter, N.1


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