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Volumn 7, Issue 4, 2008, Pages 741-791

Bernstein and De Giorgi type problems: New results via a geometric approach

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EID: 57049094392     PISSN: 0391173X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (147)

References (30)
  • 1
    • 0034957494 scopus 로고    scopus 로고
    • On a long-standing conjecture of E. De Giorgi: Symmetry in 3D for general nonlinearities and a local minimality property
    • G. ALBERTI, L. AMBROSIO and X. CABRÉ, On a long-standing conjecture of E. De Giorgi: symmetry in 3D for general nonlinearities and a local minimality property, Acta Appl. Math. 65 (2001), 9-33.
    • (2001) Acta Appl. Math , vol.65 , pp. 9-33
    • ALBERTI, G.1    AMBROSIO, L.2    CABRÉ, X.3
  • 2
    • 0347486747 scopus 로고    scopus 로고
    • 3 and a conjecture of De Giorgi, J. Amer. Math. Soc. 13 (2000) (electronic), 725-739.
    • 3 and a conjecture of De Giorgi, J. Amer. Math. Soc. 13 (2000) (electronic), 725-739.
  • 4
    • 0000340486 scopus 로고
    • Über ein geometrisches Theorem und seine Anwendung auf die partiellen Differentialgleichungen vom elliptischen Typus
    • S. BERNSTEIN, Über ein geometrisches Theorem und seine Anwendung auf die partiellen Differentialgleichungen vom elliptischen Typus, Math. Z. 26 (1927), 551-558.
    • (1927) Math. Z , vol.26 , pp. 551-558
    • BERNSTEIN, S.1
  • 5
    • 84990563948 scopus 로고
    • A gradient bound for entire solutions of quasi-linear equations and its consequences
    • L. CAFFARELLI, N. GAROFALO and F. SEGÀLA, A gradient bound for entire solutions of quasi-linear equations and its consequences, Comm. Pure Appl. Math. 47 (1994), 1457-1473.
    • (1994) Comm. Pure Appl. Math , vol.47 , pp. 1457-1473
    • CAFFARELLI, L.1    GAROFALO, N.2    SEGÀLA, F.3
  • 6
    • 5044226333 scopus 로고    scopus 로고
    • Regularity, monotonicity and symmetry of positive solutions of m-Laplace equations
    • L. DAMASCELLI and B. SCIUNZI, Regularity, monotonicity and symmetry of positive solutions of m-Laplace equations, J. Differential Equations 206 (2004), 483-515.
    • (2004) J. Differential Equations , vol.206 , pp. 483-515
    • DAMASCELLI, L.1    SCIUNZI, B.2
  • 7
    • 0036979160 scopus 로고    scopus 로고
    • Properties of entire solutions of non-uniformly elliptic equations arising in geometry and in phase transitions
    • D. DANIELLI and N. GAROFALO, Properties of entire solutions of non-uniformly elliptic equations arising in geometry and in phase transitions, Calc. Var. Partial Differential Equations 15 (2002), 451-491.
    • (2002) Calc. Var. Partial Differential Equations , vol.15 , pp. 451-491
    • DANIELLI, D.1    GAROFALO, N.2
  • 9
    • 0001472514 scopus 로고
    • 1+α local regularity of weak solutions of degenerate elliptic equations
    • 1+α local regularity of weak solutions of degenerate elliptic equations, Nonlinear Anal. 7 (1983), 827-850.
    • (1983) Nonlinear Anal , vol.7 , pp. 827-850
    • DIBENEDETTO, E.1
  • 10
    • 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
  • 11
    • 57049086933 scopus 로고    scopus 로고
    • Propriétés qualitatives de solutions d'équations et systèmes d'équations non-linéaires
    • Paris
    • A. FARINA, "Propriétés qualitatives de solutions d'équations et systèmes d'équations non-linéaires", Habilitation à diriger des recherches, Paris VI, 2002.
    • (2002) Habilitation à diriger des recherches , vol.6
    • FARINA, A.1
  • 13
    • 67649847861 scopus 로고    scopus 로고
    • A. FARINA, Liouville-type theorems for elliptic problems, In: Handbook of Differential Equations: Stationary Partial Differential Equations M. Chipot (ed.), IV Elsevier B. V., Amsterdam, 2007, 61-116.
    • A. FARINA, Liouville-type theorems for elliptic problems, In: "Handbook of Differential Equations: Stationary Partial Differential Equations" M. Chipot (ed.), Vol. IV Elsevier B. V., Amsterdam, 2007, 61-116.
  • 14
    • 60849122713 scopus 로고    scopus 로고
    • A. FARINA, B. SCIUNZI and E. VALDINOCI, Bernstein and De Giorgi type problems: new results via a geometric approach, Preliminary version of this paper, available at http://cvgmt.sns.it/ papers/, 2007.
    • A. FARINA, B. SCIUNZI and E. VALDINOCI, Bernstein and De Giorgi type problems: new results via a geometric approach, Preliminary version of this paper, available at http://cvgmt.sns.it/ papers/, 2007.
  • 15
    • 60849121595 scopus 로고    scopus 로고
    • 1D symmetry for solutions of semilinear and quasilinear elliptic equations
    • Preprint
    • A. FARINA and E. VALDINOCI, 1D symmetry for solutions of semilinear and quasilinear elliptic equations, Preprint, 2008.
    • (2008)
    • FARINA, A.1    VALDINOCI, E.2
  • 16
    • 84980187204 scopus 로고
    • The structure of complete stable minimal surfaces in 3-manifolds of nonnegative scalar curvature
    • D. FISCHER-COLBRIE and R. SCHOEN, The structure of complete stable minimal surfaces in 3-manifolds of nonnegative scalar curvature, Comm. Pure Appl. Math. 33 (1980), 199-211.
    • (1980) Comm. Pure Appl. Math , vol.33 , pp. 199-211
    • FISCHER-COLBRIE, D.1    SCHOEN, R.2
  • 17
    • 0032373311 scopus 로고    scopus 로고
    • On a conjecture of De Giorgi and some related problems
    • N. GHOUSSOUB and C. GUI, On a conjecture of De Giorgi and some related problems, Math. Ann. 311 (1998), 481-491.
    • (1998) Math. Ann , vol.311 , pp. 481-491
    • GHOUSSOUB, N.1    GUI, C.2
  • 18
    • 0041625080 scopus 로고    scopus 로고
    • Elliptic partial differential equations of second order
    • Springer-Verlag, Berlin
    • D. GILBARG and N. S. TRUDINGER, "Elliptic partial differential equations of second order", Classics in Mathematics, Springer-Verlag, Berlin, 2001.
    • (2001) Classics in Mathematics
    • GILBARG, D.1    TRUDINGER, N.S.2
  • 19
    • 0003360649 scopus 로고    scopus 로고
    • Analysis
    • of, American Mathematical Society, Providence, RI
    • E. H. LIEB and M. LOSS, "Analysis", Vol. 14 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, 1997.
    • (1997) Graduate Studies in Mathematics , vol.14
    • LIEB, E.H.1    LOSS, M.2
  • 20
    • 84990623704 scopus 로고
    • A gradient bound and a Liouville theorem for nonlinear Poisson equations
    • L. MODICA, A gradient bound and a Liouville theorem for nonlinear Poisson equations, Comm. Pure Appl. Math. 38 (1985), 679-684.
    • (1985) Comm. Pure Appl. Math , vol.38 , pp. 679-684
    • MODICA, L.1
  • 21
    • 84972514202 scopus 로고
    • Positive solutions of elliptic equations
    • W. F. MOSS and J. PIEPENBRINK, Positive solutions of elliptic equations, Pacific J. Math. 75 (1978), 219-226.
    • (1978) Pacific J. Math , vol.75 , pp. 219-226
    • MOSS, W.F.1    PIEPENBRINK, J.2
  • 23
    • 60849103265 scopus 로고
    • Bollati Boringhieri, Torino
    • E. SERNESI, "Geometria 2", Bollati Boringhieri, Torino, 1994.
    • (1994) Geometria , vol.2
    • SERNESI, E.1
  • 24
    • 60849127436 scopus 로고    scopus 로고
    • Singular Sets and Asymptotics in Geometric Analysis
    • Institut für Angewandte Mathematik, Bonn
    • L. SIMON, "Singular Sets and Asymptotics in Geometric Analysis" Lipschitz Lectures. Institut für Angewandte Mathematik, http://math.stanford.edu/~lms/lipschitz/lipschitz.pdf, Bonn, 2007.
    • (2007) Lipschitz Lectures
    • SIMON, L.1
  • 25
    • 60849097723 scopus 로고    scopus 로고
    • Fractional Laplacian phase transitions and boundary reactions: A geometric inequality and a symmetry result
    • preprint
    • Y. S. SIRE and E. VALDINOCI, Fractional Laplacian phase transitions and boundary reactions: a geometric inequality and a symmetry result, preprint, 2008.
    • (2008)
    • SIRE, Y.S.1    VALDINOCI, E.2
  • 26
    • 0032370858 scopus 로고    scopus 로고
    • Connectivity of phase boundaries in strictly convex domains
    • P. STERNBERG and K. ZUMBRUN, Connectivity of phase boundaries in strictly convex domains, Arch. Ration. Mech. Anal. 141 (1998), 375-400.
    • (1998) Arch. Ration. Mech. Anal , vol.141 , pp. 375-400
    • STERNBERG, P.1    ZUMBRUN, K.2
  • 27
    • 0032221205 scopus 로고    scopus 로고
    • A Poincaré inequality with applications to volume-constrained area-minimizing surfaces
    • P. STERNBERG and K. ZUMBRUN, A Poincaré inequality with applications to volume-constrained area-minimizing surfaces, J. Reine Angew. Math. 503 (1998), 63-85.
    • (1998) J. Reine Angew. Math , vol.503 , pp. 63-85
    • STERNBERG, P.1    ZUMBRUN, K.2
  • 28
    • 33846445540 scopus 로고
    • Regularity for a more general class of quasilinear elliptic equations
    • P. TOLKSDORF, Regularity for a more general class of quasilinear elliptic equations, J. Differential Equations 51 (1984), 126-150.
    • (1984) J. Differential Equations , vol.51 , pp. 126-150
    • TOLKSDORF, P.1
  • 29
    • 0000968617 scopus 로고
    • Regularity for a class of non-linear elliptic systems
    • K. UHLENBECK, Regularity for a class of non-linear elliptic systems, Acta Math. 138 (1977), 219-240.
    • (1977) Acta Math , vol.138 , pp. 219-240
    • UHLENBECK, K.1
  • 30
    • 33646346403 scopus 로고    scopus 로고
    • Flat level set regularity of p-Laplace phase transitions
    • vi-144
    • E. VALDINOCI, B. SCIUNZI and V. O. SAVIN, Flat level set regularity of p-Laplace phase transitions, Mem. Amer. Math. Soc. 182 (2006), vi-144.
    • (2006) Mem. Amer. Math. Soc , vol.182
    • VALDINOCI, E.1    SCIUNZI, B.2    SAVIN, V.O.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.