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Volumn 63, Issue 3, 2009, Pages 151-187

Local H1-regularity and H1/3?δ-regularity up to the boundary in time dependent viscoplasticity

Author keywords

Difference quotient technique; Interpolation; Maximal monotone operator; Model of Melan Prager; Plasticity; Regularity; Viscoplasticity

Indexed keywords

BOUNDARY REGULARITY; DIFFERENCE QUOTIENT TECHNIQUE; GENERAL CLASS; INITIAL-BOUNDARY VALUE PROBLEMS; KINEMATIC HARDENING; MAXIMAL MONOTONE OPERATOR; MONOTONE OPERATORS; PERTURBATION ESTIMATES; QUASI-STATIC; REGULARITY; TIME DEPENDENT;

EID: 70349126862     PISSN: 09217134     EISSN: None     Source Type: Journal    
DOI: 10.3233/ASY-2009-0933     Document Type: Article
Times cited : (11)

References (43)
  • 3
    • 33846946674 scopus 로고    scopus 로고
    • Quasistatic problems in viscoplasticity theory, I.models with linear hardening
    • I. Gohberg, A.F. dos Santos, F.O. Speck, F.S. Teixeira and W. Wendland, eds, Oper. Theory Adv. Appl., Vol. Birkhäuser, Basel
    • H.-D. Alber and K. Chelłmínski, Quasistatic problems in viscoplasticity theory, I.Models with linear hardening, in: Operator Theoretical Methods and Applications to Mathematical Physics, I. Gohberg, A.F. dos Santos, F.O. Speck, F.S. Teixeira and W. Wendland, eds, Oper. Theory Adv. Appl., Vol.147, Birkhäuser, Basel, 2004, pp. 105-129.
    • (2004) Operator Theoretical Methods and Applications to Mathematical Physics , vol.147 , pp. 105-129
    • Alber, H.-D.1    Chelłmínski, K.2
  • 4
    • 33847008103 scopus 로고    scopus 로고
    • Quasistatic problems in viscoplasticity theory, II. models with nonlinear hardening
    • H.-D. Alber and K. Chelłmínski, Quasistatic problems in viscoplasticity theory, II. Models with nonlinear hardening, Math. Models Meth. Appl. Sci. 17(2) (2007), 189-213.
    • (2007) Math. Models Meth. Appl. Sci. , vol.17 , Issue.2 , pp. 189-213
    • Alber, H.-D.1    Chelłmínski, K.2
  • 7
    • 27144547714 scopus 로고
    • 1 regularity
    • Boundary Value Problems for Partial Differential Equations and Applications, J.L. Lions, ed Paris
    • A. Bensoussan and J. Frehse, Asymptotic behaviour of Norton-Hoff?s law in plasticity theory and H1 regularity, in: Boundary Value Problems for Partial Differential Equations and Applications, J.L. Lions, ed., Res. Notes Appl. Math., Vol.29, Paris, 1993, pp. 3-26.
    • (1993) Res. Notes Appl. Math. , vol.29 , pp. 3-26
    • Bensoussan, A.1    Frehse, J.2
  • 8
    • 0011898456 scopus 로고    scopus 로고
    • 1 regularity
    • A. Bensoussan and J. Frehse, Asymptotic behaviour of the time dependent Norton-Hoff law in plasticity and H1 regularity, Comment. Math. Univ. Carolinae 37(2) (1996), 285-304.
    • (1996) Comment. Math. Univ. Carolinae , vol.37 , Issue.2 , pp. 285-304
    • Bensoussan, A.1    Frehse, J.2
  • 9
    • 23244453310 scopus 로고    scopus 로고
    • Regularity results for nonlinear elliptic systems and applications
    • Springer, Berlin
    • A. Bensoussan and J. Frehse, Regularity Results for Nonlinear Elliptic Systems and Applications, Appl. Math. Sci., Vol.151, Springer, Berlin, 2002.
    • (2002) Appl. Math. Sci. , vol.151
    • Bensoussan, A.1    Frehse, J.2
  • 11
    • 0004234584 scopus 로고    scopus 로고
    • Teubner-Texte zur Mathematik, Vol. Teubner, Stuttgart
    • V.I. Burenkov, Sobolev Spaces on Domains, Teubner-Texte zur Mathematik, Vol.137, Teubner, Stuttgart, 1998.
    • (1998) Sobolev Spaces on Domains , vol.137
    • Burenkov, V.I.1
  • 12
    • 0037243952 scopus 로고    scopus 로고
    • Local stress regularity in scalar nonconvex variational problems
    • C. Carstensen and S. Müller, Local stress regularity in scalar nonconvex variational problems, SIAM J. Math. Anal. 34(2) (2002), 495-509.
    • (2002) SIAM J. Math. Anal. , vol.34 , Issue.2 , pp. 495-509
    • Carstensen, C.1    Müller, S.2
  • 14
    • 70349115431 scopus 로고    scopus 로고
    • Regularity of the stresses in prandtl-reuss perfect plasticity
    • available at: Preprint
    • A. Demyanov, Regularity of the stresses in Prandtl-Reuss perfect plasticity, SISSA Trieste, Preprint, 2007, available at: http://hdl.handle.net/ 1963/1963.
    • (2007) SISSA Trieste
    • Demyanov, A.1
  • 18
    • 0016433301 scopus 로고
    • Sur les matériaux standards généralisés
    • B. Halphen and N. Quoc Son, Sur les matériaux standards généralisés, J. Méc. 14 (1975), 39-63.
    • (1975) J. Méc. , vol.14 , pp. 39-63
    • Halphen, B.1    Quoc Son, N.2
  • 19
    • 33750801997 scopus 로고    scopus 로고
    • Regularity results for quasilinear elliptic systems of power-law growth in nonsmooth domains
    • PhD thesis, Stuttgart
    • D. Knees, Regularity results for quasilinear elliptic systems of power-law growth in nonsmooth domains. Boundary, transmission and crack problems, PhD thesis, Stuttgart, 2004.
    • (2004) Boundary, Transmission and Crack Problems
    • Knees, D.1
  • 20
    • 33746280539 scopus 로고    scopus 로고
    • Global regularity of the elastic fields of a power-law model on lipschitz domains
    • D. Knees, Global regularity of the elastic fields of a power-law model on Lipschitz domains, Math. Methods. Appl. Sci. 29 (2006), 1363-1391.
    • (2006) Math. Methods. Appl. Sci. , vol.29 , pp. 1363-1391
    • Knees, D.1
  • 21
    • 70349129326 scopus 로고    scopus 로고
    • Short note on global spatial regularity in elasto-plasticity with linear hardening
    • D. Knees, Short note on global spatial regularity in elasto-plasticity with linear hardening, Manuscript, 2008.
    • (2008) Manuscript
    • Knees, D.1
  • 28
    • 61849100952 scopus 로고    scopus 로고
    • Regularity up to the boundary for nonlinear elliptic systems arising in time-incremental infinitesimal elasto-plasticity
    • P. Neff and D. Knees, Regularity up to the boundary for nonlinear elliptic systems arising in time-incremental infinitesimal elasto-plasticity, SIAM J. Math. Anal. 40(1) (2008), 21-43.
    • (2008) SIAM J. Math. Anal. , vol.40 , Issue.1 , pp. 21-43
    • Neff, P.1    Knees, D.2
  • 30
    • 39449090735 scopus 로고    scopus 로고
    • Homogenization in viscoplasticity
    • S. Nesenenko, Homogenization in viscoplasticity, SIAM J. Math. Anal. 39(1) (2007), 236-262.
    • (2007) SIAM J. Math. Anal. , vol.39 , Issue.1 , pp. 236-262
    • Nesenenko, S.1
  • 32
    • 0002002145 scopus 로고
    • Spannungsverteilung in plastischen Körpern
    • Delft. (Gesammelte Abhandlungen, Springer, Berlin, 1961, pp. 133-148.)
    • L. Prandtl, Spannungsverteilung in plastischen Körpern, in: Proc. Int. Congr. Appl. Mech., Delft 1924, 1925, pp. 43-54. (Gesammelte Abhandlungen, Springer, Berlin, 1961, pp. 133-148.)
    • (1924) Proc. Int. Congr. Appl. Mech. , vol.1925 , pp. 43-54
    • Prandtl, L.1
  • 33
    • 0030494614 scopus 로고    scopus 로고
    • Errors of finite element method for perfectly elasto-plastic problems
    • S.I. Repin, Errors of finite element method for perfectly elasto-plastic problems, Math. Models Meth. Appl. Sci. 6(5) (1996), 587-604.
    • (1996) Math. Models Meth. Appl. Sci. , vol.6 , Issue.5 , pp. 587-604
    • Repin, S.I.1
  • 34
    • 84914985370 scopus 로고
    • Berücksichtigung der elastischen Formänderung in der Plastizitätstheorie
    • A. Reuss, Berücksichtigung der elastischen Formänderung in der Plastizitätstheorie, Z. Angew. Math. Mech. 10 (1930), 266-274.
    • (1930) Z. Angew. Math. Mech. , vol.10 , pp. 266-274
    • Reuss, A.1
  • 35
    • 85090531975 scopus 로고    scopus 로고
    • Nonlinear Partial Differential Equations with Applications
    • Birkhäuser, Basel
    • T. Roubǐcek, Nonlinear Partial Differential Equations with Applications, Int. Ser. Numer. Math., Vol.153, Birkhäuser, Basel, 2005.
    • (2005) Int. Ser. Numer. Math. , vol.153
    • Roubǐcek, T.1
  • 36
    • 0003291397 scopus 로고    scopus 로고
    • Monotone operators in banach spaces and nonlinear partial differential equations
    • AMS, Providence, RI
    • E. Showalter, Monotone Operators in Banach Spaces and Nonlinear Partial Differential Equations, Math. Surveys Monogr., Vol.49, AMS, Providence, RI, 1997.
    • (1997) Math. Surveys Monogr , vol.49
    • Showalter, E.1
  • 37
    • 0010219843 scopus 로고
    • Differentiability of local extremals of variational problems in the mechanics of perfect elastoplastic media
    • (English translation in Differential Equations 23 (1987), 1349-1358.)
    • G.A. Seregin, Differentiability of local extremals of variational problems in the mechanics of perfect elastoplastic media, Differents. Uravn. 23 (1987), 1981-1991. (English translation in Differential Equations 23 (1987), 1349-1358.)
    • (1987) Differents. Uravn. , vol.23 , pp. 1981-1991
    • Seregin, G.A.1
  • 38
    • 24244463504 scopus 로고
    • A local Caccioppoli-type estimate for extremals of variational problems in Hencky plasticity
    • Novosibirsk (in Russian)
    • G.A. Seregin, A local Caccioppoli-type estimate for extremals of variational problems in Hencky plasticity, in: Some Applications of Functional Analysis to Problems of Mathematical Physics, Novosibirsk, 1988, pp. 127-138 (in Russian).
    • (1988) Some Applications of Functional Analysis to Problems of Mathematical Physics , pp. 127-138
    • Seregin, G.A.1
  • 39
    • 0347408009 scopus 로고
    • On regularity of weak solutions of variational problems in plasticity theory
    • G.A. Seregin, On regularity of weak solutions of variational problems in plasticity theory, Algebra Analiz 2 (1990), 121-140.
    • (1990) Algebra Analiz , vol.2 , pp. 121-140
    • Seregin, G.A.1
  • 40
    • 33746278222 scopus 로고    scopus 로고
    • Remarks on regularity up to the boundary for solutions to variational problems in plasticity theory
    • G.A. Seregin, Remarks on regularity up to the boundary for solutions to variational problems in plasticity theory, J. Math. Sci. 93(5) (1999), 779-783.
    • (1999) J. Math. Sci. , vol.93 , Issue.5 , pp. 779-783
    • Seregin, G.A.1
  • 43
    • 0003432644 scopus 로고
    • Boundary Value Problems of Finite Elasticity. Local Theorems on Existence, Uniqueness and Analytic Dependence on Data
    • Springer, New York
    • T. Valent, Boundary Value Problems of Finite Elasticity. Local Theorems on Existence, Uniqueness and Analytic Dependence on Data, Springer Tracts in Natural Philosophy, Vol.31, Springer, New York, 1988.
    • (1988) Springer Tracts in Natural Philosophy , vol.31
    • Valent, T.1


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