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Measurable solutions for elliptic and evolution inclusions

  • * Kenneth Kuttler

    * Kenneth Kuttler

I would like to thank the anonymous referees for finding some loose ends and things which needed improvement.

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  • This paper obtains existence of random variable solutions to elliptic and evolution inclusions. As a special case, surprising theorems are obtained for the quasistatic problems. A new existence theorem is also presented for evolution inclusions with set valued operators dependent on elements of a measurable space.

    Mathematics Subject Classification: Primary: 35R60; Secondary: 35Q74, 60H25.

    Citation:

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  • [1] K. T. AndrewsK. L. KuttlerJ. Li and M. Shillor, Measurable solutions for elliptic inclusions and quasistatic problems, Comput. Math. Appl., 77 (2019), 2869-2882.  doi: 10.1016/j.camwa.2018.09.025.
    [2] A. Bensoussan and R. Temam, Équations stochastiques du type Navier-Stokes, J. Functional Analysis, 13 (1973), 195-222.  doi: 10.1016/0022-1236(73)90045-1.
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    [7] K. L. Kuttler, J. Li and M. Shillor, A general product measurability theorem with applications to variational inequalities, Electron. J. Differential Equations, 90 (2016), 12 pp.
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    [9] K. Kuttler, Non-degenerate implicit evolution inclusions, Electron. J. Differential Equations, 34 (2000), 20 pp.
    [10] K. L. Kuttler and M. Shillor, Set-valued pseudomonotone maps and degenerate evolution inclusions, Commun. Contemp. Math., 1 (1999), 87-123.  doi: 10.1142/S0219199799000067.
    [11] J.-L. Lions, Quelques Méthods de Résolution des Problèmes aux Limites Non Linéaires, Dunod; Gauthier-Villars, Paris, 1969.
    [12] S. Migórski, A. Ochal and M. Sofonea, Nonlinear Inclusions and Hemivariational Inequalities. Models and Analysis of Contact Problems, Vol. 26, Advances in Mechanics and Mathematics, Springer, New York, 2013. doi: 10.1007/978-1-4614-4232-5.
    [13] M. Shillor, M. Sofonea and J. J. Telega, Models and Analysis of Quasistatic Contact, Vol. 655, Lecture Notes in Physics, Springer, Berlin, Heidelberg, 2004. doi: 10.1007/b99799.
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