Regularity results for parabolic systems related to a class of non-newtonian fluids

Acerbi, E; Mingione, G; Seregin, G. A.

doi:10.1016/j.anihpc.2002.11.002

Acerbi, E ; Mingione, G ; Seregin, G. A.

Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) no. 1, pp. 25-60.

MR Zbl | 5 citations dans Numdam

DOI : 10.1016/j.anihpc.2002.11.002

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Acerbi, E; Mingione, G; Seregin, G. A. Regularity results for parabolic systems related to a class of non-newtonian fluids. Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) no. 1, pp. 25-60. doi : 10.1016/j.anihpc.2002.11.002. https://www.numdam.org/articles/10.1016/j.anihpc.2002.11.002/

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Bögelein, Verena; Duzaar, Frank Hölder estimates for parabolic p(x, t)-Laplacian systems, Mathematische Annalen, Volume 354 (2012) no. 3, p. 907 | DOI:10.1007/s00208-011-0750-4
Baroni, Paolo Regularity in parabolic Dini continuous systems, Forum Mathematicum, Volume 23 (2011) no. 6 | DOI:10.1515/form.2011.049
Alkhutov, Yu. A.; Zhikov, V. V. Hölder continuity of solutions of parabolic equations with variable nonlinearity exponent, Journal of Mathematical Sciences, Volume 179 (2011) no. 3, p. 347 | DOI:10.1007/s10958-011-0599-9
Lang, Honglei; Liu, Changchun; Li, Zhenbang Some properties of solutions for an evolution p(x)-Laplacian equation, Lobachevskii Journal of Mathematics, Volume 32 (2011) no. 1, p. 48 | DOI:10.1134/s1995080211010082
ZHANG, CHAO; ZHOU, SHULIN ENTROPY AND RENORMALIZED SOLUTIONS FOR THEp(x)-LAPLACIAN EQUATION WITH MEASURE DATA, Bulletin of the Australian Mathematical Society, Volume 82 (2010) no. 3, p. 459 | DOI:10.1017/s0004972710000432
Alkhutov, Yu. A.; Zhikov, V. V. Existence theorems and qualitative properties of solutions to parabolic equations with a variable order of nonlinearity, Doklady Mathematics, Volume 81 (2010) no. 1, p. 34 | DOI:10.1134/s1064562410010114
Zhang, Chao; Zhou, Shulin Renormalized and entropy solutions for nonlinear parabolic equations with variable exponents and L1 data, Journal of Differential Equations, Volume 248 (2010) no. 6, p. 1376 | DOI:10.1016/j.jde.2009.11.024
Fu, Yongqiang; Yu, Mei The Neumann boundary value problem of higher order quasilinear elliptic equation, Nonlinear Analysis: Theory, Methods Applications, Volume 72 (2010) no. 12, p. 4488 | DOI:10.1016/j.na.2010.02.024
Harjulehto, Petteri; Hästö, Peter; Lê, Út V.; Nuortio, Matti Overview of differential equations with non-standard growth, Nonlinear Analysis: Theory, Methods Applications, Volume 72 (2010) no. 12, p. 4551 | DOI:10.1016/j.na.2010.02.033
Bögelein, Verena; Parviainen, Mikko Self-improving property of nonlinear higher order parabolic systems near the boundary, Nonlinear Differential Equations and Applications NoDEA, Volume 17 (2010) no. 1, p. 21 | DOI:10.1007/s00030-009-0038-5
Alkhutov, Yu. A.; Zhikov, V. V. Existence theorems for solutions of parabolic equations with variable order of nonlinearity, Proceedings of the Steklov Institute of Mathematics, Volume 270 (2010) no. 1, p. 15 | DOI:10.1134/s0081543810030028
Antontsev, S.; Shmarev, S. On the blow-up of solutions to anisotropic parabolic equations with variable nonlinearity, Proceedings of the Steklov Institute of Mathematics, Volume 270 (2010) no. 1, p. 27 | DOI:10.1134/s008154381003003x
Bögelein, Verena Partial regularity and singular sets of solutions of higher order parabolic systems, Annali di Matematica Pura ed Applicata, Volume 188 (2009) no. 1, p. 61 | DOI:10.1007/s10231-008-0067-4
Fu, Yongqiang The principle of concentration compactness in spaces and its application, Nonlinear Analysis: Theory, Methods Applications, Volume 71 (2009) no. 5-6, p. 1876 | DOI:10.1016/j.na.2009.01.023
Lian, Songzhe; Gao, Wenjie; Cao, Chunling; Yuan, Hongjun Study of the solutions to a model porous medium equation with variable exponent of nonlinearity, Journal of Mathematical Analysis and Applications, Volume 342 (2008) no. 1, p. 27 | DOI:10.1016/j.jmaa.2007.11.046
Antontsev, S. N.; Shmarev, S. I. Existence and uniqueness of solutions of degenerate parabolic equations with variable exponents of nonlinearity, Journal of Mathematical Sciences, Volume 150 (2008) no. 5, p. 2289 | DOI:10.1007/s10958-008-0129-6
Antontsev, S.; Shmarev, S. Extinction of solutions of parabolic equations with variable anisotropic nonlinearities, Proceedings of the Steklov Institute of Mathematics, Volume 261 (2008) no. 1, p. 11 | DOI:10.1134/s0081543808020028
Bögelein, Verena; Zatorska-Goldstein, Anna Higher integrability of very weak solutions of systems of p(x)-Laplacean type, Journal of Mathematical Analysis and Applications, Volume 336 (2007) no. 1, p. 480 | DOI:10.1016/j.jmaa.2007.02.019
Antontsev, Stanislav; Shmarev, Sergey Chapter 1 Elliptic equations with anisotropic nonlinearity and nonstandard growth conditions, Volume 3 (2006), p. 1 | DOI:10.1016/s1874-5733(06)80005-7
Mingione, Giuseppe Regularity of minima: An invitation to the dark side of the calculus of variations, Applications of Mathematics, Volume 51 (2006) no. 4, p. 355 | DOI:10.1007/s10778-006-0110-3
Antontsev, S.; Shmarev, S. Parabolic Equations with Anisotropic Nonstandard Growth Conditions, Free Boundary Problems, Volume 154 (2006), p. 33 | DOI:10.1007/978-3-7643-7719-9_4
Antontsev, Stanislav; Shmarev, Sergei Elliptic equations and systems with nonstandard growth conditions: Existence, uniqueness and localization properties of solutions, Nonlinear Analysis: Theory, Methods Applications, Volume 65 (2006) no. 4, p. 728 | DOI:10.1016/j.na.2005.09.035
Zhang, Qihu A strong maximum principle for differential equations with nonstandard p(x)-growth conditions, Journal of Mathematical Analysis and Applications, Volume 312 (2005) no. 1, p. 24 | DOI:10.1016/j.jmaa.2005.03.013
Antontsev, S.N.; Shmarev, S.I. A model porous medium equation with variable exponent of nonlinearity: existence, uniqueness and localization properties of solutions, Nonlinear Analysis: Theory, Methods Applications, Volume 60 (2005) no. 3, p. 515 | DOI:10.1016/j.na.2004.09.026

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