메뉴 건너뛰기




Volumn , Issue 546, 2002, Pages 73-138

Optimal interior and boundary regularity for almost minimizers to elliptic variational integrals

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0036265561     PISSN: 00754102     EISSN: None     Source Type: Journal    
DOI: 10.1515/crll.2002.046     Document Type: Article
Times cited : (148)

References (46)
  • 2
    • 0001246518 scopus 로고
    • On the first variation of a varifold
    • [All2]
    • [All2] Allard, W. K., On the first variation of a varifold, Ann. Math. 95 (1972), 417-491.
    • (1972) Ann. Math. , vol.95 , pp. 417-491
    • Allard, W.K.1
  • 3
    • 0000575237 scopus 로고
    • On the first variation of a varifold: Boundary behaviour
    • [All3]
    • [All3] Allard, W. K., On the first variation of a varifold: boundary behaviour, Ann. Math. 101 (1975), 418-446.
    • (1975) Ann. Math. , vol.101 , pp. 418-446
    • Allard, W.K.1
  • 4
    • 0000557474 scopus 로고
    • Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and singularity structure
    • [Alm1]
    • [Alm1] Almgren, F. J., Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and singularity structure, Ann. Math. 87 (1968), 321-391.
    • (1968) Ann. Math. , vol.87 , pp. 321-391
    • Almgren, F.J.1
  • 5
    • 0000910006 scopus 로고
    • Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints
    • [Alm2]
    • [Alm2] Almgren, F. J., Existence and regularity almost everywhere of solutions to elliptic variational problems with constraints, Mem. Amer. Math. Soc. 165 (1976).
    • (1976) Mem. Amer. Math. Soc. , vol.165
    • Almgren, F.J.1
  • 7
    • 84966241483 scopus 로고
    • and Almgren's big regularity paper, World Scientific, Singapore
    • [Alm3] Almgren, F. J., ℚ-valued functions minimizing Dirichlet's integral and the regularity of area minimizing rectifiable currents up to codimension two, Princeton Univ. 1984, 3745 g; see also Bull. Amer. Math. Soc. 8 (1983), 327-328 and Almgren's big regularity paper, ed. Scheffer, V., Taylor, J. E., World Scientific, Singapore 2000.
    • (1983) Bull. Amer. Math. Soc. , vol.8 , pp. 327-328
    • Scheffer, V.1    Taylor, J.E.2
  • 8
    • 0040261320 scopus 로고
    • Optimal isoperimetric inequalities
    • [Alm4]
    • [Alm4] Almgren, F. J., Optimal isoperimetric inequalities, Indiana Univ. Math. J. 35 (1986), 451-547.
    • (1986) Indiana Univ. Math. J. , vol.35 , pp. 451-547
    • Almgren, F.J.1
  • 9
    • 0002533813 scopus 로고
    • Regularity theory for almost minimal currents
    • [Bo]
    • [Bo] Bombieri, E., Regularity theory for almost minimal currents. Arch. Rat. Mech. Anal. 7 (1982), 99-130.
    • (1982) Arch. Rat. Mech. Anal. , vol.7 , pp. 99-130
    • Bombieri, E.1
  • 10
    • 84972493906 scopus 로고
    • The structure of solutions to Plateau's problem in the n-sphere
    • [Br1]
    • [Br1] Brothers, J. E., The structure of solutions to Plateau's problem in the n-sphere, J. Diff. Geom. 11 (1976), 387-400.
    • (1976) J. Diff. Geom. , vol.11 , pp. 387-400
    • Brothers, J.E.1
  • 11
    • 0043290109 scopus 로고
    • Existence and structure of tangent cones at the boundary of an area minimizing integral current
    • [Br2]
    • [Br2] Brothers, J. E., Existence and structure of tangent cones at the boundary of an area minimizing integral current, Indiana Univ. Math. J. 26 (1977), 1027-1044.
    • (1977) Indiana Univ. Math. J. , vol.26 , pp. 1027-1044
    • Brothers, J.E.1
  • 13
    • 0002876921 scopus 로고    scopus 로고
    • Frontiere orientate di misura minima
    • [DeG]
    • [DeG] DeGiorgi, E., Frontiere orientate di misura minima, Sem. Mat. Norm. Sup. Pisa, 1960-61.
    • Sem. Mat. Norm. Sup. Pisa , pp. 1960-1961
    • DeGiorgi, E.1
  • 14
    • 85011604828 scopus 로고
    • On the existence of surfaces with prescribed mean curvature and boundary in higher dimensions
    • [Du1]
    • [Du1] Duzaar, F., On the existence of surfaces with prescribed mean curvature and boundary in higher dimensions, Anal, non lin. 10 (1993), 191-214.
    • (1993) Anal, Non Lin. , vol.10 , pp. 191-214
    • Duzaar, F.1
  • 15
    • 0043290106 scopus 로고    scopus 로고
    • Boundary regularity for area minimizing currents with prescribed volume
    • [Du2]
    • [Du2] Duzaar, F., Boundary regularity for area minimizing currents with prescribed volume, J. Geom. Anal. 7 (1997), 585-592.
    • (1997) J. Geom. Anal. , vol.7 , pp. 585-592
    • Duzaar, F.1
  • 16
    • 51249176240 scopus 로고
    • On the existence of integral currents with prescribed mean curvature vector
    • [DF1]
    • [DF1] Duzaar, F., Fuchs, M., On the existence of integral currents with prescribed mean curvature vector, Manuscr. math. 67 (1990), 41-67.
    • (1990) Manuscr. Math. , vol.67 , pp. 41-67
    • Duzaar, F.1    Fuchs, M.2
  • 17
    • 0002328858 scopus 로고
    • A general existence theorem for integral currents with prescribed mean curvature form
    • [DF2]
    • [DF2] Duzaar, F., Fuchs, M., A general existence theorem for integral currents with prescribed mean curvature form, Boll. U.M.I. (7) 6-B (1992), 901-912.
    • (1992) Boll. U.M.I. (7) , vol.6 B , pp. 901-912
    • Duzaar, F.1    Fuchs, M.2
  • 18
    • 0036002543 scopus 로고    scopus 로고
    • Nonlinear elliptic systems with Dini continuous coefficients
    • [DGa]
    • [DGa] Duzaar, F., Gastel, A., Nonlinear elliptic systems with Dini continuous coefficients, Arch. Math. 78 (2002), 58-73.
    • (2002) Arch. Math. , vol.78 , pp. 58-73
    • Duzaar, F.1    Gastel, A.2
  • 19
    • 0034555619 scopus 로고    scopus 로고
    • Optimal interior partial regularity for nonlinear elliptic systems: The method of A-harmonic approximation
    • [DGr]
    • [DGr] Duzaar, F., Grotowski, J. F., Optimal interior partial regularity for nonlinear elliptic systems: The method of A-harmonic approximation, Manuscr. Math. 103 (2000), 267-298.
    • (2000) Manuscr. Math. , vol.103 , pp. 267-298
    • Duzaar, F.1    Grotowski, J.F.2
  • 20
    • 0034559768 scopus 로고    scopus 로고
    • Partial regularity for almost minimizing functions of quasiconvex integrands
    • [DGG]
    • [DGG] Duzaar, F., Gastel, A., Grotowski, J. F., Partial regularity for almost minimizing functions of quasiconvex integrands, SIAM J. Math. Anal. 32 (2000), 665-687.
    • (2000) SIAM J. Math. Anal. , vol.32 , pp. 665-687
    • Duzaar, F.1    Gastel, A.2    Grotowski, J.F.3
  • 21
    • 0002221434 scopus 로고
    • λ minimizing currents
    • [DS1]
    • [DS1] Duzaar, F., Steffen, K., λ minimizing currents, Manuscr. math. 80 (1993), 403-447.
    • (1993) Manuscr. Math. , vol.80 , pp. 403-447
    • Duzaar, F.1    Steffen, K.2
  • 22
    • 0001359668 scopus 로고
    • Boundary regularity for minimizing currents with prescribed mean curvature
    • [DS2]
    • [DS2] Duzaar, F., Steffen, K., Boundary regularity for minimizing currents with prescribed mean curvature, Calc. Var. 1 (1993), 355-406.
    • (1993) Calc. Var. , vol.1 , pp. 355-406
    • Duzaar, F.1    Steffen, K.2
  • 23
    • 0002026379 scopus 로고    scopus 로고
    • Existence of hypersurfaces with prescribed mean curvature in Riemannian manifolds
    • [DS3]
    • [DS3] Duzaar, F., Steffen, K., Existence of hypersurfaces with prescribed mean curvature in Riemannian manifolds, Indiana Univ. Math. J. 45 (1996), 1045-1093.
    • (1996) Indiana Univ. Math. J. , vol.45 , pp. 1045-1093
    • Duzaar, F.1    Steffen, K.2
  • 24
    • 0003418232 scopus 로고
    • [Fe], Springer-Verlag, Berlin-Heidelberg-New York
    • [Fe] Federer, H., Geometric measure theory, Springer-Verlag, Berlin-Heidelberg-New York 1969.
    • (1969) Geometric Measure Theory
    • Federer, H.1
  • 25
    • 84966226124 scopus 로고
    • The singular set of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension
    • [Fe1]
    • [Fe1] Federer, H., The singular set of area minimizing rectifiable currents with codimension one and of area minimizing flat chains modulo two with arbitrary codimension, Bull. Amer. Math. Soc. 76 (1970), 767771.
    • (1970) Bull. Amer. Math. Soc. , vol.76 , pp. 767-771
    • Federer, H.1
  • 27
    • 0002246356 scopus 로고
    • On the regularity of boundaries of sets minimizing perimeter with a volume constraint
    • [GMT]
    • [GMT] Gonzalez, E., Massari, U., Tamanini, I., On the regularity of boundaries of sets minimizing perimeter with a volume constraint, Indiana Univ. Math. J. 32 (1983), 25-37.
    • (1983) Indiana Univ. Math. J. , vol.32 , pp. 25-37
    • Gonzalez, E.1    Massari, U.2    Tamanini, I.3
  • 28
    • 0042789065 scopus 로고
    • On boundary regularity for integral currents or flat chains modulo two minimizing the integral of an elliptic integrand
    • [Ha1]
    • [Ha1] Hardt, R., On boundary regularity for integral currents or flat chains modulo two minimizing the integral of an elliptic integrand, Comm. Part. Diff. Equ. 2 (1977), 1163-1232.
    • (1977) Comm. Part. Diff. Equ. , vol.2 , pp. 1163-1232
    • Hardt, R.1
  • 29
    • 0042287995 scopus 로고
    • Uniqueness of nonparametric area minimizing currents
    • [Ha2]
    • [Ha2] Hardt, R., Uniqueness of nonparametric area minimizing currents, Indiana Univ. Math. J. 26 (1977), 65-71.
    • (1977) Indiana Univ. Math. J. , vol.26 , pp. 65-71
    • Hardt, R.1
  • 31
    • 0001752645 scopus 로고
    • Boundary regularity and embedded solutions for the oriented Plateau problem
    • [HS]
    • [HS] Hardt, R., Simon, L., Boundary regularity and embedded solutions for the oriented Plateau problem, Ann. Math. 110 (1979), 439-486.
    • (1979) Ann. Math. , vol.110 , pp. 439-486
    • Hardt, R.1    Simon, L.2
  • 34
    • 0013478565 scopus 로고
    • Minimal surfaces of codimension one
    • [MM], North-Holland. Amsterdam
    • [MM] Massari, U., Miranda, M., Minimal surfaces of codimension one, Math. stud. 91, North-Holland. Amsterdam 1984.
    • (1984) Math. Stud. , vol.91
    • Massari, U.1    Miranda, M.2
  • 35
    • 51249187629 scopus 로고
    • Frontiere orientate con ostacoli
    • [Mi]
    • [Mi] Miranda, M., Frontiere orientate con ostacoli, Ann. Univ. Ferrara 16 (1971), 29-37.
    • (1971) Ann. Univ. Ferrara , vol.16 , pp. 29-37
    • Miranda, M.1
  • 36
    • 84967773286 scopus 로고
    • A sharp counterexample on the regularity of Φ-minimizing hypersurfaces
    • [Morg]
    • [Morg] Morgan, F., A sharp counterexample on the regularity of Φ-minimizing hypersurfaces, Bull. Amer. Math. Soc. 22 (1990), 295-299.
    • (1990) Bull. Amer. Math. Soc. , vol.22 , pp. 295-299
    • Morgan, F.1
  • 38
    • 0011346267 scopus 로고
    • A new proof of the regularity for rectifiable currents which minimize parametric elliptic functionals
    • [SS]
    • [SS] Schoen, R., Simon, L., A new proof of the regularity for rectifiable currents which minimize parametric elliptic functionals, Indiana Univ. Math. J. 31 (1982), 413-434.
    • (1982) Indiana Univ. Math. J. , vol.31 , pp. 413-434
    • Schoen, R.1    Simon, L.2
  • 39
    • 34250289052 scopus 로고
    • Regularity and singularity estimates on hypersurfaces minimizing parametric elliptic variational integrals
    • [SSA]
    • [SSA] Schoen, R., Simon, L., Almgren, F. J., Regularity and singularity estimates on hypersurfaces minimizing parametric elliptic variational integrals, Acta Math. 139 (1977), 217-265.
    • (1977) Acta Math. , vol.139 , pp. 217-265
    • Schoen, R.1    Simon, L.2    Almgren, F.J.3
  • 40
    • 0001841087 scopus 로고
    • Lectures on geometric measure theory
    • [Si1], ANU Canberra
    • [Si1] Simon, L., Lectures on geometric measure theory, Proc. CMA 3, ANU Canberra, 1983.
    • (1983) Proc. CMA , vol.3
    • Simon, L.1
  • 42
    • 0037801570 scopus 로고
    • Quasiconvex functions with subquadratic growth
    • [Sv1]
    • [Sv1] Šverak, V., Quasiconvex functions with subquadratic growth, Proc. Roy. Soc. London A 433 (1991), 223-225.
    • (1991) Proc. Roy. Soc. London A , vol.433 , pp. 223-225
    • Šverak, V.1
  • 43
    • 84974157879 scopus 로고
    • Rank-one convexity does not imply quasiconvexity
    • [Sv2]
    • [Sv2] Sverak, V., Rank-one convexity does not imply quasiconvexity, Proc. Roy. Soc. Edinburgh 120 (1992), 185-189.
    • (1992) Proc. Roy. Soc. Edinburgh , vol.120 , pp. 185-189
    • Sverak, V.1
  • 45
    • 0001862636 scopus 로고
    • Boundaries of Cacciopoli sets with Hölder-continuous normal vector
    • [Ta2]
    • [Ta2] Tamanini, I., Boundaries of Cacciopoli sets with Hölder-continuous normal vector, J. reine angew. Math. 334 (1982), 27-39.
    • (1982) J. Reine Angew. Math. , vol.334 , pp. 27-39
    • Tamanini, I.1
  • 46
    • 51249171649 scopus 로고
    • Variational problems of least area type with constraints
    • [Ta3]
    • [Ta3] Tamanini, I., Variational problems of least area type with constraints, Ann. Univ. Ferrara 34 (1988), 183-217.
    • (1988) Ann. Univ. Ferrara , vol.34 , pp. 183-217
    • Tamanini, I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.