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Volumn 18, Issue 4, 2003, Pages 373-400

Bounds for the singular set of solutions to non linear elliptic systems

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EID: 0347622554     PISSN: 09442669     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00526-003-0209-x     Document Type: Article
Times cited : (70)

References (30)
  • 1
    • 0001515752 scopus 로고
    • A regularity theorem for minimizers of quasiconvex integrals
    • Acerbi, E., Fusco, N.: A regularity theorem for minimizers of quasiconvex integrals. Arch. Rational Mech. Anal. 99, 261-281 (1987)
    • (1987) Arch. Rational Mech. Anal. , vol.99 , pp. 261-281
    • Acerbi, E.1    Fusco, N.2
  • 2
    • 33646883627 scopus 로고
    • Regularity of minimizers of non-quadratic functionals: The case 1 < p < 2
    • Acerbi, E., Fusco, N.: Regularity of minimizers of non-quadratic functionals: the case 1 < p < 2. J. Math. Anal. Appl. 140, 115-135 (1989)
    • (1989) J. Math. Anal. Appl. , vol.140 , pp. 115-135
    • Acerbi, E.1    Fusco, N.2
  • 5
    • 0037788410 scopus 로고
    • Hölder continuity of the solutions of some nonlinear elliptic systems
    • Campanato, S.: Hölder continuity of the solutions of some nonlinear elliptic systems. Adv. in Math. 48, 16-43 (1983)
    • (1983) Adv. in Math. , vol.48 , pp. 16-43
    • Campanato, S.1
  • 6
    • 0347490441 scopus 로고
    • Qualche risultato recente di regolarità per sistemi differenziali in ipotesi di monotonia
    • Campanato, S.: Qualche risultato recente di regolarità per sistemi differenziali in ipotesi di monotonia. Boll. Un. Mat. Ital. A (7) 2, 27-57 (1988)
    • (1988) Boll. Un. Mat. Ital. A (7) , vol.2 , pp. 27-57
    • Campanato, S.1
  • 7
    • 0346859949 scopus 로고
    • Differentiability of the solutions of nonlinear elliptic systems with natural growth
    • Campanato, S.: Differentiability of the solutions of nonlinear elliptic systems with natural growth. Ann. Mat. Pura Appl. (4) 131, 75-106 (1982)
    • (1982) Ann. Mat. Pura Appl. (4) , vol.131 , pp. 75-106
    • Campanato, S.1
  • 8
    • 0000657529 scopus 로고
    • Un esempio di estremali discontinue per un problema variazionale di tipo ellittico
    • De Giorgi, E.: Un esempio di estremali discontinue per un problema variazionale di tipo ellittico. Boll. Un. Mat. Ital. 1(4), 135-137 (1968)
    • (1968) Boll. Un. Mat. Ital. , vol.1 , Issue.4 , pp. 135-137
    • De Giorgi, E.1
  • 9
    • 0013027253 scopus 로고    scopus 로고
    • Optimal partial regularity for nonlinear elliptic systems of higher order
    • Duzaar, F., Gastel, A., Grotowski, J.F.: Optimal partial regularity for nonlinear elliptic systems of higher order. J. Math. Sci. Univ. Tokyo 8, 463-499 (2001)
    • (2001) J. Math. Sci. Univ. Tokyo , vol.8 , pp. 463-499
    • Duzaar, F.1    Gastel, A.2    Grotowski, J.F.3
  • 10
    • 0034555619 scopus 로고    scopus 로고
    • Optimal interior partial regularity for nonlinear elliptic systems: The method of A-harmonic approximation
    • Duzaar, F., Grotowski, J.F.: Optimal interior partial regularity for nonlinear elliptic systems: the method of A-harmonic approximation. Manuscripta Math. 103, 267-298 (2000)
    • (2000) Manuscripta Math. , vol.103 , pp. 267-298
    • Duzaar, F.1    Grotowski, J.F.2
  • 11
    • 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. 546, 73-138 (2002)
    • (2002) J. Reine Angew. Math. , vol.546 , pp. 73-138
    • Duzaar, F.1    Steffen, K.2
  • 12
    • 0000184055 scopus 로고
    • Quasiconvexity and partial regularity in the calculus of variations
    • Evans, L.C.: Quasiconvexity and partial regularity in the calculus of variations. Arch. Rational Mech. Anal. 95, 227-252 (1986)
    • (1986) Arch. Rational Mech. Anal. , vol.95 , pp. 227-252
    • Evans, L.C.1
  • 13
    • 0003283911 scopus 로고
    • Multiple integrals in the calculus of variations and nonlinear elliptic systems
    • Princeton University Press, Princeton
    • Giaquinta, M.: Multiple integrals in the calculus of variations and nonlinear elliptic systems. Annals of mathematics studies, 105. Princeton University Press, Princeton 1983
    • (1983) Annals of Mathematics Studies , vol.105
    • Giaquinta, M.1
  • 14
    • 0000496328 scopus 로고
    • Nonlinear elliptic systems with quadratic growth
    • Giaquinta, M., Giusti, E.: Nonlinear elliptic systems with quadratic growth. Manuscripta Math. 24, 323-349 (1978)
    • (1978) Manuscripta Math. , vol.24 , pp. 323-349
    • Giaquinta, M.1    Giusti, E.2
  • 15
    • 0001472207 scopus 로고
    • Almost-everywhere regularity for solutions of nonlinear elliptic systems
    • Giaquinta, M., Modica, G.: Almost-everywhere regularity for solutions of nonlinear elliptic systems. Manuscripta Math. 28, 109-158 (1979)
    • (1979) Manuscripta Math. , vol.28 , pp. 109-158
    • Giaquinta, M.1    Modica, G.2
  • 17
    • 0036876820 scopus 로고    scopus 로고
    • Boundary regularity for nonlinear elliptic systems
    • Grotowski, J.F.: Boundary regularity for nonlinear elliptic systems. Calc. Var. 15, 353-388 (2002)
    • (2002) Calc. Var. , vol.15 , pp. 353-388
    • Grotowski, J.F.1
  • 18
    • 0036956557 scopus 로고    scopus 로고
    • Boundary regularity for quasilinear elliptic systems
    • Grotowski, J.F.: Boundary regularity for quasilinear elliptic systems. Comm. Partial Differential Equations 27, 2491-2512 (2002)
    • (2002) Comm. Partial Differential Equations , vol.27 , pp. 2491-2512
    • Grotowski, J.F.1
  • 19
    • 0013001298 scopus 로고
    • Quasimonotonicity, regularity and duality for nonlinear systems of partial differential equations
    • Hamburger, C.: Quasimonotonicity, regularity and duality for nonlinear systems of partial differential equations. Ann. Mat. Pura Appl. 169(4), 321-354 (1995)
    • (1995) Ann. Mat. Pura Appl. , vol.169 , Issue.4 , pp. 321-354
    • Hamburger, C.1
  • 20
    • 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 Math. 95, 11-31 (1998)
    • (1998) Manuscripta Math. , vol.95 , pp. 11-31
    • Hamburger, C.1
  • 21
    • 0012549640 scopus 로고
    • Some regularity results for quasilinear elliptic systems of second order
    • Hildebrandt, S., Widman, K.O.: Some regularity results for quasilinear elliptic systems of second order. Math. Z. 142, 67-86 (1975)
    • (1975) Math. Z. , vol.142 , pp. 67-86
    • Hildebrandt, S.1    Widman, K.O.2
  • 22
    • 0011663530 scopus 로고
    • On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order
    • Hildebrandt, S., Widman, K.O.: On the Hölder continuity of weak solutions of quasilinear elliptic systems of second order. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 4(4), 145-178 (1977)
    • (1977) Ann. Scuola Norm. Sup. Pisa Cl. Sci. , vol.4 , Issue.4 , pp. 145-178
    • Hildebrandt, S.1    Widman, K.O.2
  • 23
    • 0037832743 scopus 로고
    • Regularitätsuntersuchungen von lo>sungen elliptiscer systeme von quasilinearen differetialgleichungen zweiter Ordnung
    • Ivert, P.A.: Regularitätsuntersuchungen von lo>sungen elliptiscer systeme von quasilinearen differetialgleichungen zweiter Ordnung. Manuscripta Math. 30, 53-88 (1979)
    • (1979) Manuscripta Math. , vol.30 , pp. 53-88
    • Ivert, P.A.1
  • 25
    • 0038610614 scopus 로고    scopus 로고
    • The singular set of solutions to non-differentiable elliptic systems
    • Mingione, G.: The singular set of solutions to non-differentiable elliptic systems. Arch. Rational Mech. Anal. 166, 287-301 (2003)
    • (2003) Arch. Rational Mech. Anal. , vol.166 , pp. 287-301
    • Mingione, G.1
  • 26
    • 0348120578 scopus 로고
    • Example of an irregular solution to a nonlinear elliptic system with analytic coefficients and conditions for regularity. Theory of nonlinear operators
    • Acad. Sci., Berlin
    • Necas, J.: Example of an irregular solution to a nonlinear elliptic system with analytic coefficients and conditions for regularity. Theory of nonlinear operators (Proc. Fourth Internat. Summer School, Acad. Sci., Berlin, 1975), pp. 197-206
    • (1975) Proc. Fourth Internat. Summer School , pp. 197-206
    • Necas, J.1
  • 27
    • 0001521609 scopus 로고
    • Higher integrabilty from reverse Hölder inequalities
    • Stredulinsky, E.W.: Higher integrabilty from reverse Hölder inequalities. Indiana U. Math. J. 29, 407-413 (1980)
    • (1980) Indiana U. Math. J. , vol.29 , pp. 407-413
    • Stredulinsky, E.W.1
  • 28
    • 0037510797 scopus 로고    scopus 로고
    • A singular minimizer of a smooth strongly convex functional in three dimensions
    • Šverák, V., Yan, X.: A singular minimizer of a smooth strongly convex functional in three dimensions. Calc. Var. 10, 213-221 (2000)
    • (2000) Calc. Var. , vol.10 , pp. 213-221
    • Šverák, V.1    Yan, X.2
  • 29
    • 0037180551 scopus 로고    scopus 로고
    • Non Lipschitz minimizers of smooth uniformly convex variational integrals
    • Šverák, V., Yan, X.: Non Lipschitz minimizers of smooth uniformly convex variational integrals. Proc. Nat. Acad. Sci. USA 99(24), 15269-15276 (2002)
    • (2002) Proc. Nat. Acad. Sci. USA , vol.99 , Issue.24 , pp. 15269-15276
    • Šverák, V.1    Yan, X.2
  • 30
    • 0000968617 scopus 로고
    • Regularity for a class of non-linear elliptic systems
    • Uhlenbeck, K.: Regularity for a class of non-linear elliptic systems. Acta Math. 138, 219-240 (1977)
    • (1977) Acta Math. , vol.138 , pp. 219-240
    • Uhlenbeck, K.1


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