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Volumn 214, Issue 1005, 2011, Pages 1-128

Parabolic systems with polynomial growth and regularity

Author keywords

Higher integrability; Parabolic systems; Regularity; Singular sets

Indexed keywords


EID: 80054097536     PISSN: 00659266     EISSN: 19476221     Source Type: Journal    
DOI: 10.1090/S0065-9266-2011-00614-3     Document Type: Article
Times cited : (153)

References (77)
  • 1
    • 27844601209 scopus 로고    scopus 로고
    • Gradient estimates for the p (x)-Laplacean system
    • MR2155087 2006f:35068
    • Acerbi, E., Mingione, G.: Gradient estimates for the p (x)-Laplacean system. J. reine ang. Math. (Crelles J.) 584(2005), 117-148. MR2155087 (2006f:35068)
    • (2005) J. Reine Ang. Math. (Crelles J.) , vol.584 , pp. 117-148
    • Acerbi, E.1    Mingione, G.2
  • 2
    • 33846833574 scopus 로고    scopus 로고
    • Gradient estimates for a class of parabolic systems
    • MR2286632 2007k:35211
    • Acerbi, E., Mingione, G.: Gradient estimates for a class of parabolic systems. Duke Math. J. 136(2007), 285-320. MR2286632 (2007k:35211)
    • (2007) Duke Math. J. , vol.136 , pp. 285-320
    • Acerbi, E.1    Mingione, G.2
  • 3
    • 0842308385 scopus 로고    scopus 로고
    • Regularity results for parabolic systems related to a class of Non Newtonian fluids
    • MR2037246 2005a:35118
    • Acerbi, E., Mingione, G., Seregin, G. A.: Regularity results for parabolic systems related to a class of Non Newtonian fluids. Ann. Inst. H. Poincaré Anal. Non Linèaire 21(2004), 25-60. MR2037246 (2005a:35118)
    • (2004) Ann. Inst. H. Poincaré Anal. Non Linèaire , vol.21 , pp. 25-60
    • Acerbi, E.1    Mingione, G.2    Seregin, G.A.3
  • 4
    • 84876720817 scopus 로고
    • A note on Riesz potentials
    • MR0458158 56:16361
    • Adams, D. R.: A note on Riesz potentials. Duke Math. J. 42(1975), 765-778. MR0458158 (56:16361)
    • (1975) Duke Math. J. , vol.42 , pp. 765-778
    • Adams, D.R.1
  • 5
    • 77954342203 scopus 로고    scopus 로고
    • Sobolev spaces. Second edition
    • Elsevier/Academic Press, Amsterdam, MR2424078 2009e:46025
    • Adams, R. A., Fournier, J. J. F.: Sobolev spaces. Second edition. Pure and Applied Mathematics, 140. Elsevier/Academic Press, Amsterdam, 2003. MR2424078 (2009e:46025)
    • (2003) Pure and Applied Mathematics , vol.140
    • Adams, R.A.1    Fournier, J.J.F.2
  • 6
    • 0001323666 scopus 로고
    • Un Théoreme de compacite
    • MR0152860 27:2832
    • Aubin, J. P.: Un Théoreme de compacite. C. R. Acad. Sci. Paris 256(1963), 5042-5044. MR0152860 (27:2832)
    • (1963) C. R. Acad. Sci. Paris , vol.256 , pp. 5042-5044
    • Aubin, J.P.1
  • 7
    • 59949101181 scopus 로고    scopus 로고
    • Higher integrability for weak solutions of higher order degenerate parabolic systems
    • MR2431372 2009c:35199
    • Bögelein, V.: Higher integrability for weak solutions of higher order degenerate parabolic systems. Ann. Acad. Sci. Fenn. Ser. A I 33(2008), 387-412. MR2431372 (2009c:35199)
    • (2008) Ann. Acad. Sci. Fenn. Ser. A I , vol.33 , pp. 387-412
    • Bögelein, V.1
  • 8
    • 52349122581 scopus 로고    scopus 로고
    • Partial regularity and singular sets of solutions of higher order parabolic systems
    • MR2447930 2009k:35117
    • Bogelein, V.: Partial regularity and singular sets of solutions of higher order parabolic systems. Ann. Mat. Pura Appl. (4) 188(2009), 61-122. MR2447930 (2009k:35117)
    • (2009) Ann. Mat. Pura Appl , vol.188 , Issue.4 , pp. 61-122
    • Bogelein, V.1
  • 9
    • 77950368652 scopus 로고    scopus 로고
    • Very weak solutions of higher-order degenerate parabolic systems
    • MR2478931 2010e:35128
    • Bogelein, V.: Very weak solutions of higher-order degenerate parabolic systems. Adv. Differential Equations 14(2009), 121-200. MR2478931 (2010e:35128)
    • (2009) Adv. Differential Equations , vol.14 , pp. 121-200
    • Bogelein, V.1
  • 14
    • 84871414400 scopus 로고
    • 1,2 solvability for the Cauchy-Dirichlet problem for parabolic equations with VMO coefficients
    • MR1239929 94j:35180
    • 1,2 solvability for the Cauchy-Dirichlet problem for parabolic equations with VMO coefficients. Comm. Part. Diff. Equ. 18(1993), 1735-1763. MR1239929 (94j:35180)
    • (1993) Comm. Part. Diff. Equ. , vol.18 , pp. 1735-1763
    • Bramanti, M.1    Cerutti, M.C.2
  • 15
    • 11144322175 scopus 로고    scopus 로고
    • Parabolic equations with BMO coefficients in Lipschitz domains
    • MR2110205 2005i:35106
    • Byun, S. S.: Parabolic equations with BMO coefficients in Lipschitz domains. J. Differential Equations 209(2005), 229-265. MR2110205 (2005i:35106)
    • (2005) J. Differential Equations , vol.209 , pp. 229-265
    • Byun, S.S.1
  • 16
    • 53349117250 scopus 로고    scopus 로고
    • Fourth-order parabolic equations with weak BMO coefficients in Reifenberg domains
    • MR2460025 2009i:35133
    • Byun, S. S., Wang, L.: Fourth-order parabolic equations with weak BMO coefficients in Reifenberg domains. J. Differential Equations 245(2008), 3217-3252. MR2460025 (2009i:35133)
    • (2008) J. Differential Equations , vol.245 , pp. 3217-3252
    • Byun, S.S.1    Wang, L.2
  • 17
    • 0041125729 scopus 로고    scopus 로고
    • 1, p estimates for elliptic equations in divergence form
    • MR1486629 99c:35053
    • 1, p estimates for elliptic equations in divergence form. Comm. Pure Appl. Math. 51(1998), 1-21. MR1486629 (99c:35053)
    • (1998) Comm. Pure Appl. Math. , vol.51 , pp. 1-21
    • Caffarelli, L.1    Peral, I.2
  • 19
    • 0008992698 scopus 로고
    • On the nonlinear parabolic systems in divergence form. Hölder continuity and partial Hölder continuity of the solutions
    • MR772253 86c:35072
    • Campanato, S.: On the nonlinear parabolic systems in divergence form. Hölder continuity and partial Hölder continuity of the solutions. Ann. Mat. Pura Appl. (IV), 137(1984), 83-122. MR772253 (86c:35072)
    • (1984) Ann. Mat. Pura Appl. (IV) , vol.137 , pp. 83-122
    • Campanato, S.1
  • 20
    • 34347171922 scopus 로고
    • θ) (Ω, δ) e loro proprietà
    • MR0192330 33:556
    • θ) (Ω, δ) e loro proprietà. Ann. Mat. Pura Appl. (IV), 69(1965), 383-392. MR0192330 (33:556)
    • (1965) Ann. Mat. Pura Appl. (IV) , vol.69 , pp. 383-392
    • Da Prato, G.1
  • 22
    • 0000657529 scopus 로고
    • Un esempio di estremali discontinue per un problema variazionale di tipo ellittico
    • MR0227827 37:3411
    • De Giorgi, E.: Un esempio di estremali discontinue per un problema variazionale di tipo ellittico. Boll. Unione Mat. Ital. (IV), 1(1968), 135-137. MR0227827 (37:3411)
    • (1968) Boll. Unione Mat. Ital. , vol.1 , Issue.4 , pp. 135-137
    • De Giorgi, E.1
  • 23
    • 0001168467 scopus 로고
    • On the local behaviour of solutions of degenerate parabolic equations with measurable coefficients
    • MR881103 89a:35118
    • Di Benedetto, E.: On the local behaviour of solutions of degenerate parabolic equations with measurable coefficients. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (IV) 13(1986), 487-535. MR881103 (89a:35118)
    • (1986) Ann. Scuola Norm. Sup. Pisa Cl. Sci. , vol.13 , Issue.4 , pp. 487-535
    • Di Benedetto, E.1
  • 24
    • 0348034313 scopus 로고
    • Intrinsic Harnack type inequalities for solutions of certain degenerate parabolic equations
    • MR913961 88j:35082
    • Di Benedetto, E.: Intrinsic Harnack type inequalities for solutions of certain degenerate parabolic equations. Arch. Rational Mech. Anal. 100(1988), 129-147. MR913961 (88j:35082)
    • (1988) Arch. Rational Mech. Anal. , vol.100 , pp. 129-147
    • Di Benedetto, E.1
  • 25
    • 0004109586 scopus 로고
    • Universitext. New York, NY: Springer-Verlag, MR1230384 94h:35130
    • Di Benedetto, E.: Degenerate parabolic equations. Universitext. New York, NY: Springer-Verlag. xv, 387 (1993). MR1230384 (94h:35130)
    • (1993) Degenerate Parabolic Equations , vol.15 , pp. 387
    • Di Benedetto, E.1
  • 26
    • 84941461568 scopus 로고
    • Regularity of solutions of nonlinear degenerate parabolic systems
    • MR743967 85j:35089
    • Di Benedetto, E., Friedman, A.: Regularity of solutions of nonlinear degenerate parabolic systems. J. reine ang. Math. (Crelles J.) 349(1984), 83-128. MR743967 (85j:35089)
    • (1984) J. Reine Ang. Math. (Crelles J.) , vol.349 , pp. 83-128
    • Di Benedetto, E.1    Friedman, A.2
  • 27
    • 84961469235 scopus 로고
    • Hölder estimates for nonlinear degenerate parabolic systems
    • MR783531 87f:35134a
    • Di Benedetto, E., Friedman, A.: Hölder estimates for nonlinear degenerate parabolic systems. J. reine ang. Math. (Crelles J.) 357(1985), 1-22. MR783531 (87f:35134a)
    • (1985) J. Reine Ang. Math. (Crelles J.) , vol.357 , pp. 1-22
    • Di Benedetto, E.1    Friedman, A.2
  • 28
    • 0009396335 scopus 로고
    • On the higher integrability of the gradient of weak solutions of certain degenerate elliptic systems
    • MR1246185 94i:35077
    • Di Benedetto, E., Manfredi, J. J.: On the higher integrability of the gradient of weak solutions of certain degenerate elliptic systems. Amer. J. Math. 115(1993), 1107-1134. MR1246185 (94i:35077)
    • (1993) Amer. J. Math. , vol.115 , pp. 1107-1134
    • Di Benedetto, E.1    Manfredi, J.J.2
  • 30
    • 33846993418 scopus 로고    scopus 로고
    • The existence of regular boundary points for nonlinear elliptic systems
    • MR2300451 2008b:35057
    • Duzaar, F., Kristensen, J., Mingione, G.: The existence of regular boundary points for nonlinear elliptic systems. J. reine angew. Math. (Crelles J.) 602(2007), 17-58. MR2300451 (2008b:35057)
    • (2007) J. Reine Angew. Math. (Crelles J.) , vol.602 , pp. 17-58
    • Duzaar, F.1    Kristensen, J.2    Mingione, G.3
  • 31
    • 3042673947 scopus 로고    scopus 로고
    • The p-harmonic approximation and the regularity of p-harmonic maps
    • DOI 10.1007/s00526-003-0233-x
    • Duzaar, F., Mingione, G.: The p-harmonic approximation and the regularity of p-harmonic maps. Calc. Var. Partial Differ. Equ. 20(2004), 235-256. MR2062943 (2005d:35094) (Pubitemid 38808914)
    • (2004) Calculus of Variations and Partial Differential Equations , vol.20 , Issue.3 , pp. 235-256
    • Duzaar, F.1    Mingione, G.2
  • 32
    • 4344636919 scopus 로고    scopus 로고
    • Regularity for degenerate elliptic problems via p-harmonic approximation
    • MR2086757 2005h:35128
    • Duzaar, F., Mingione, G.: Regularity for degenerate elliptic problems via p-harmonic approximation. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 21(2004), 735-766. MR2086757 (2005h:35128)
    • (2004) Ann. Inst. Henri Poincaré, Anal. Non Linéaire , vol.21 , pp. 735-766
    • Duzaar, F.1    Mingione, G.2
  • 33
    • 25644433664 scopus 로고    scopus 로고
    • Systemes paraboliques de la deuxieme ordre, regularité optimale, et des ensembles singuliers des solutions
    • DOI 10.1016/j.anihpc.2004.10.011, PII S0294144905000338
    • Duzaar, F., Mingione, G.: Second order parabolic systems, optimal regularity, and singular sets of solutions. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 22(2005), 705-751. MR2172857 (2008h:35139) (Pubitemid 41383968)
    • (2005) Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis , vol.22 , Issue.6 , pp. 705-751
    • Duzaar, F.1    Mingione, G.2
  • 34
    • 57749083373 scopus 로고    scopus 로고
    • Harmonic type approximation lemmas
    • MR2499905 2010e:35022
    • Duzaar, F., Mingione, G.: Harmonic type approximation lemmas. J. Math. Anal. Appl. 352(2009), 301-335. MR2499905 (2010e:35022)
    • (2009) J. Math. Anal. Appl. , vol.352 , pp. 301-335
    • Duzaar, F.1    Mingione, G.2
  • 36
    • 77956188654 scopus 로고    scopus 로고
    • Gradient estimates via linear and non-linear potentials
    • MR2719282
    • Duzaar, F., Mingione, G.: Gradient estimates via linear and non-linear potentials. Journal of Functional Analysis 259(2010), 2961-2998. MR2719282
    • (2010) Journal of Functional Analysis , vol.259 , pp. 2961-2998
    • Duzaar, F.1    Mingione, G.2
  • 37
    • 0036265561 scopus 로고    scopus 로고
    • Optimal interior and boundary regularity for almost minimizers to elliptic variational integrals
    • Duzaar, F., Steffen, K.: Optimal interior and boundary regularity for almost minimizers to elliptic variational integrals. J. reine angew. Math. (Crelles J.) 546(2002), 73-138. MR1900994 (2003b:49038) (Pubitemid 36932374)
    • (2002) Journal fur die Reine und Angewandte Mathematik , Issue.546 , pp. 73-138
    • Duzaar, F.1    Steffen, K.2
  • 38
    • 0033588750 scopus 로고    scopus 로고
    • Higher integrability for minimizers of integral functionals with (p, q) growth
    • MR1713266 2000h:49055
    • Esposito, L., Leonetti, F., Mingione, G.: Higher integrability for minimizers of integral functionals with (p, q) growth. J. Differential Equations 157(1999), 414-438. MR1713266 (2000h:49055)
    • (1999) J. Differential Equations , vol.157 , pp. 414-438
    • Esposito, L.1    Leonetti, F.2    Mingione, G.3
  • 39
    • 0003283911 scopus 로고
    • Multiple integrals in the calculus of variations and nonlinear elliptic systems
    • Princeton University Press, Princeton, NJ, MR717034 86b:49003
    • Giaquinta, M.: Multiple integrals in the calculus of variations and nonlinear elliptic systems. Annals of Mathematics Studies, 105. Princeton University Press, Princeton, NJ, 1983. MR717034 (86b:49003)
    • (1983) Annals of Mathematics Studies , vol.105
    • Giaquinta, M.1
  • 41
    • 0003130403 scopus 로고
    • Regularity of differential forms minimizing degenerate elliptic functionals
    • MR1179331 93i:49049
    • Hamburger, C.: Regularity of differential forms minimizing degenerate elliptic functionals. J. reine angew. Math. (Crelles J.) 431(1992), 7-64. MR1179331 (93i:49049)
    • (1992) J. Reine Angew. Math. (Crelles J.) , vol.431 , pp. 7-64
    • Hamburger, C.1
  • 42
    • 0031643979 scopus 로고    scopus 로고
    • A new partial regularity proof for solutions of nonlinear elliptic systems
    • Hamburger, C.: A new partial regularity proof for solutions of nonlinear elliptic systems. manuscripta mathematica 95(1998), 11-31. MR1492366 (98m:35055) (Pubitemid 128339518)
    • (1998) Manuscripta Mathematica , vol.95 , Issue.1 , pp. 11-31
    • Hamburger, C.1
  • 43
    • 0011725080 scopus 로고    scopus 로고
    • An example of irregular solution to a nonlinear Euler-Lagrange elliptic system with real analytic coefficients
    • MR1401417 97e:35050
    • Hao, W., Leonardi S., Necas J.: An example of irregular solution to a nonlinear Euler-Lagrange elliptic system with real analytic coefficients. Ann. Scu. Norm. Sup. Pisa Cl. Sci. (IV) 23(1996), 57-67. MR1401417 (97e:35050)
    • (1996) Ann. Scu. Norm. Sup. Pisa Cl. Sci. , vol.23 , Issue.4 , pp. 57-67
    • Hao, W.1    Leonardi, S.2    Necas, J.3
  • 44
    • 0000417913 scopus 로고
    • p-estimates for degenerated elliptic operators
    • MR722254 85i:46037
    • p-estimates for degenerated elliptic operators. Studia Math. 75(1983), 293-312. MR722254 (85i:46037)
    • (1983) Studia Math. , vol.75 , pp. 293-312
    • Iwaniec, T.1
  • 46
    • 0039398554 scopus 로고    scopus 로고
    • On the regularity of weak solutions to parabolic systems in two spatial dimensions
    • John, O., Stará, J.: On the regularity of weak solutions to parabolic systems in two spatial dimensions. Comm. Part. Diff. Equ. 23(1998), 1159-1170. MR1642595 (99k:35079) (Pubitemid 128364048)
    • (1998) Communications in Partial Differential Equations , vol.23 , Issue.7-8 , pp. 1159-1170
    • John, O.1    Stara, J.2
  • 47
    • 84860611777 scopus 로고    scopus 로고
    • On the existence of time derivative of weak solutions to parabolic systems
    • Varenna, R. Salvi ed., Harlow: Longman. Pitman Res. Notes Math. Ser, MR1773597 2001f:35181
    • John, O., Stará, J.: On the existence of time derivative of weak solutions to parabolic systems. Navier-Stokes equations. Theory and numerical methods. Proceedings of the international conference, Varenna, 1997, R. Salvi ed., Harlow: Longman. Pitman Res. Notes Math. Ser. 388(1998), 193-200. MR1773597 (2001f:35181)
    • (1997) Navier-Stokes Equations. Theory and Numerical Methods. Proceedings of the International Conference , vol.388 , pp. 193-200
    • John, O.1    Stará, J.2
  • 48
    • 0034165209 scopus 로고    scopus 로고
    • Higher integrability for parabolic systems of p-Laplacian type
    • MR1749438 2001b:35152
    • Kinnunen, J., Lewis, J. L.: Higher integrability for parabolic systems of p-Laplacian type. Duke Math. J. 102(2000), 253-271. MR1749438 (2001b:35152)
    • (2000) Duke Math. J. , vol.102 , pp. 253-271
    • Kinnunen, J.1    Lewis, J.L.2
  • 49
    • 0036552277 scopus 로고    scopus 로고
    • Very weak solutions of parabolic systems of p-Laplacian type
    • MR1948889 2003j:35138
    • Kinnunen, J., Lewis, J. L.: Very weak solutions of parabolic systems of p-Laplacian type. Ark. Mat. 40(2002), 105-132. MR1948889 (2003j:35138)
    • (2002) Ark. Mat. , vol.40 , pp. 105-132
    • Kinnunen, J.1    Lewis, J.L.2
  • 50
    • 33744951323 scopus 로고    scopus 로고
    • Summability of semicontinuous supersolutions to a quasilinear parabolic equation
    • Kinnunen, J., Lindqvist, P.: Summability of semicontinuous supersolutions to a quasilinear parabolic equation. Ann. Sc. Norm. Super. Pisa Cl. Sci. (V) 4(2005), 59-78. MR2165403 (2006j:35114) (Pubitemid 43853351)
    • (2005) Annali della Scuola Normale - Classe di Scienze , vol.4 , Issue.1 , pp. 59-78
    • Kinnunen, J.1    Lindqvist, P.2
  • 51
    • 0033475519 scopus 로고    scopus 로고
    • A local estimate for nonlinear equations with discontinuous coefficients
    • MR1720770 2000k:35084
    • Kinnunen, J., Zhou, S.: A local estimate for nonlinear equations with discontinuous coefficients, Comm. Part. Diff. Equ. 24(1999), 2043-2068. MR1720770 (2000k:35084)
    • (1999) Comm. Part. Diff. Equ. , vol.24 , pp. 2043-2068
    • Kinnunen, J.1    Zhou, S.2
  • 52
    • 33645686460 scopus 로고    scopus 로고
    • The singular set of minima of integral functionals
    • DOI 10.1007/s00205-005-0402-5
    • Kristensen, J., Mingione, G.: The singular set of minima of integral functionals. Arch. Rat. Mech. Anal. 180(2006), 331-398. MR2214961 (2007d:49059) (Pubitemid 43536188)
    • (2006) Archive for Rational Mechanics and Analysis , vol.180 , Issue.3 , pp. 331-398
    • Kristensen, J.1    Mingione, G.2
  • 53
    • 77957236075 scopus 로고    scopus 로고
    • Boundary regularity in variational problems
    • MR2721587
    • Kristensen, J., Mingione, G.: Boundary regularity in variational problems. Arch. Rat. Mech. Anal. 198(2010), 369-455 MR2721587
    • (2010) Arch. Rat. Mech. Anal. , vol.198 , pp. 369-455
    • Kristensen, J.1    Mingione, G.2
  • 54
    • 0009941105 scopus 로고    scopus 로고
    • Partial regularity results for minimizers of quasiconvex functionals of higher order
    • MR1902546 2003e:49055
    • Kronz, M.: Partial regularity results for minimizers of quasiconvex functionals of higher order. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 19(2002), 81-112. MR1902546 (2003e:49055)
    • (2002) Ann. Inst. Henri Poincaré, Anal. Non Linéaire , vol.19 , pp. 81-112
    • Kronz, M.1
  • 55
    • 33947167707 scopus 로고    scopus 로고
    • Parabolic and elliptic equations with VMO coefficients
    • MR2304157 2008a:35125
    • Krylov, N.: Parabolic and Elliptic Equations with VMO Coefficients. Comm. Part. Diff. Equ. 32(2007), 453475. MR2304157 (2008a:35125)
    • (2007) Comm. Part. Diff. Equ. , vol.32 , pp. 453475
    • Krylov, N.1
  • 58
    • 38249029124 scopus 로고
    • Regularity for minima of functionals with p-growth
    • MR969420 90e:49015
    • Manfredi, J. J.: Regularity for minima of functionals with p-growth. J. Differential Equations 76(1988), 203-212. MR969420 (90e:49015)
    • (1988) J. Differential Equations , vol.76 , pp. 203-212
    • Manfredi, J.J.1
  • 60
    • 0018059032 scopus 로고
    • Integral inequalities of Poincaré and Wirtinger type
    • MR0493308 58:12336
    • Meyers, N. G.: Integral inequalities of Poincaré and Wirtinger type. Arch. Rational Mech. Anal. 68(1978), 113-120. MR0493308 (58:12336)
    • (1978) Arch. Rational Mech. Anal. , vol.68 , pp. 113-120
    • Meyers, N.G.1
  • 61
    • 0038610614 scopus 로고    scopus 로고
    • The singular set of solutions to non-differentiable elliptic systems
    • DOI 10.1007/s00205-002-0231-8
    • Mingione, G.: The singular set of solutions to non-differentiable elliptic systems. Arch. Rat. Mech. Anal. 166(2003), 287-301. MR1961442 (2004b:35070) (Pubitemid 36754971)
    • (2003) Archive for Rational Mechanics and Analysis , vol.166 , Issue.4 , pp. 287-301
    • Mingione, G.1
  • 62
    • 0347622554 scopus 로고    scopus 로고
    • Bounds for the singular set of solutions to non linear elliptic systems
    • DOI 10.1007/s00526-003-0209-x
    • Mingione, G.: Bounds for the singular set of solutions to non linear elliptic systems. Calc. Var. Partial Differ. Equ. 18(2003), 373-400. MR2020367 (2004i:35121) (Pubitemid 37550875)
    • (2003) Calculus of Variations and Partial Differential Equations , vol.18 , Issue.4 , pp. 373-400
    • Mingione, G.1
  • 63
    • 84867971666 scopus 로고    scopus 로고
    • Regularity of minima: An invitation to the dark side of the calculus of variations
    • DOI 10.1007/s10778-006-0110-3
    • Mingione, G.: Regularity of minima: an invitation to the dark side of the Calculus of Variations. Applications of Mathematics 51(2006), 355-425. MR2291779 (2007k:35086) (Pubitemid 44282637)
    • (2006) Applications of Mathematics , vol.51 , Issue.4 , pp. 355-425
    • Mingione, G.1
  • 64
    • 35448932506 scopus 로고    scopus 로고
    • The Calderón-Zygmund theory for elliptic problems with measure data
    • MR2352517 2008i:35102
    • Mingione, G.: The Calderón-Zygmund theory for elliptic problems with measure data. Ann. Scu. Norm. Sup. Pisa Cl. Sci. (V) 6(2007), 195-261. MR2352517 (2008i:35102)
    • (2007) Ann. Scu. Norm. Sup. Pisa Cl. Sci. , vol.6 , Issue.5 , pp. 195-261
    • Mingione, G.1
  • 65
    • 38849128264 scopus 로고    scopus 로고
    • Singularities of minima: A walk on the wild side of the Calculus of Variations
    • DOI 10.1007/s10898-007-9226-1, Variational Analysis and Partial Differential Equations. In memory of Sergio Campanato and Guido Stampacchia
    • Mingione, G.: Singularities of minima: a walk on the wild side of the Calculus of Variations. J. Global Optim. 40(2008), 209-223. MR2373553 (2008k:35089) (Pubitemid 351189550)
    • (2008) Journal of Global Optimization , vol.40 , Issue.1-3 , pp. 209-223
    • Mingione, G.1
  • 66
    • 73249152185 scopus 로고    scopus 로고
    • Gradient estimates below the duality exponent
    • MR2578563 2011a:35136
    • Mingione, G.: Gradient estimates below the duality exponent. Mathematische Annalen 346(2010), 571-627 MR2578563 (2011a:35136)
    • (2010) Mathematische Annalen , vol.346 , pp. 571-627
    • Mingione, G.1
  • 67
    • 78751520354 scopus 로고    scopus 로고
    • Gradient potential estimates
    • Mingione, G.: Gradient potential estimates. J. European Math. Soc. 13(2011), 459-486.
    • (2011) J. European Math. Soc. , vol.13 , pp. 459-486
    • Mingione, G.1
  • 68
    • 0036882769 scopus 로고    scopus 로고
    • Partial regularity results for evolutional p-Laplacian systems with natural growth
    • MR1946712 2004a:35074
    • Misawa, M.: Partial regularity results for evolutional p-Laplacian systems with natural growth. Manuscr. Math. 109(2002), 419-454. MR1946712 (2004a:35074)
    • (2002) Manuscr. Math. , vol.109 , pp. 419-454
    • Misawa, M.1
  • 69
    • 0013077563 scopus 로고    scopus 로고
    • Local Hölder regularity of gradients for evolutional p-Laplacian systems
    • DOI 10.1007/s102310100044
    • Misawa, M.: Local Hölder regularity of gradients for evolutional p-Laplacian systems. Ann. Mat. Pura Appl (IV) 181(2002), 389-405. MR1939688 (2003h:35100) (Pubitemid 44228818)
    • (2002) Annali di Matematica Pura ed Applicata , vol.181 , Issue.4 , pp. 389-405
    • Misawa, M.1
  • 70
    • 25644441144 scopus 로고    scopus 로고
    • On the Hölder continuity of weak solutions to nonlinear parabolic systems in two space dimensions
    • MR1651938 99h:35091
    • Naumann, J., Wolf, J., Wolff, M.: On the Hölder continuity of weak solutions to nonlinear parabolic systems in two space dimensions. Commentat. Math. Univ. Carol. 39(1998), 237-255. MR1651938 (99h:35091)
    • (1998) Commentat. Math. Univ. Carol. , vol.39 , pp. 237-255
    • Naumann, J.1    Wolf, J.2    Wolff, M.3
  • 71
    • 34250112428 scopus 로고
    • p (0, T; B)
    • MR916688 89c:46055
    • p (0, T; B). Ann. Mat. Pura Appl. (IV) 146(1987), 65-96. MR916688 (89c:46055)
    • (1987) Ann. Mat. Pura Appl. , vol.146 , Issue.4 , pp. 65-96
    • Simon, J.1
  • 73
    • 0000963105 scopus 로고
    • Counterexample to the regularity of weak solution of the quasilinear parabolic system
    • MR843425 87j:35190
    • Stará, J., John, O., Malý, J.: Counterexample to the regularity of weak solution of the quasilinear parabolic system. Commentat. Math. Univ. Carol. 27(1986), 123-136. MR843425 (87j:35190)
    • (1986) Commentat. Math. Univ. Carol. , vol.27 , pp. 123-136
    • Stará, J.1    John, O.2    Malý, J.3
  • 74
    • 0000581771 scopus 로고
    • On the Hölder continuity of bounded weak solutions of quasilinear parabolic systems
    • MR627929 83c:35022
    • Struwe, M.: On the Hölder continuity of bounded weak solutions of quasilinear parabolic systems. Manuscr. Math. 35(1981), 125-145. MR627929 (83c:35022)
    • (1981) Manuscr. Math. , vol.35 , pp. 125-145
    • Struwe, M.1
  • 75
    • 0037180551 scopus 로고    scopus 로고
    • Non Lipschitz minimizers of smooth uniformly convex variational integrals
    • MR1946762 2003h:49066
    • Sverák, V., Yan, X.: Non Lipschitz minimizers of smooth uniformly convex variational integrals. Proc. Nat. Acad. Sci. USA 99(24) (2002), 15268-15276. MR1946762 (2003h:49066)
    • (2002) Proc. Nat. Acad. Sci. USA , vol.99 , Issue.24 , pp. 15268-15276
    • Sverák, V.1    Yan, X.2
  • 76
    • 0000968617 scopus 로고
    • Regularity for a class of non-linear elliptic systems
    • MR0474389 57:14031
    • Uhlenbeck, K.: Regularity for a class of non-linear elliptic systems. Acta Math. 138(1977), 219-240. MR0474389 (57:14031)
    • (1977) Acta Math. , vol.138 , pp. 219-240
    • Uhlenbeck, K.1
  • 77
    • 0000200173 scopus 로고
    • α-regularity of the gradient of solutions of degenerate parabolic systems
    • MR886719 89g:35057
    • α-regularity of the gradient of solutions of degenerate parabolic systems. Ann. Mat. Pura Appl. (IV) 145(1986), 385-405. MR886719 (89g:35057)
    • (1986) Ann. Mat. Pura Appl. , vol.145 , Issue.4 , pp. 385-405
    • Wiegner, M.1


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