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Boundary value problem for elliptic differential equations in non-commutative cases

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  • This paper is devoted to abstract second order complete elliptic differential equations set on $\left[ 0,1\right] $ in non-commutative cases. Existence, uniqueness and maximal regularity of the strict solution are proved. The study is performed in $C^{\theta }\left( \left[ 0,1\right] ;X\right) $.
    Mathematics Subject Classification: 35A09, 35B65, 35C15, 35J25, 35R20, 47D06.


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  • [1]

    G. Da Prato, Abstract differential equations, maximal regularity and linearization, in "Nonlinear Functional Analysis and its Applications, Part 1 (Berkeley, Calif., 1983)," Proc. Sympos. Pure Math., 45, Amer. Math. Soc., Providence, RI (1986), 359-370.


    G. Da Prato and P. Grisvard, Sommes d'opérateurs linéaires et équations différentielles opérationnelles, J. Math. Pures Appl. (9), 54 (1975), 305-387.


    A. Favini, R. Labbas, S. Maingot and M. Meisner, Study of complete abstract elliptic differential equations in non-commutative cases, Appl. Anal., 91 (2012), 1495-1510.doi: 10.1080/00036811.2011.635652.


    A. Favini, R. Labbas, S. Maingot, H. Tanabe and A. Yagi, Necessary and sufficient conditions for maximal regularity in the study of elliptic differential equations in Hölder spaces, Discrete Contin. Dyn. Syst., 22 (2008), 973-987.doi: 10.3934/dcds.2008.22.973.


    P. Grisvard, Spazi di tracce e applicazioni, Rend. Mat. (6), 5 (1972), 657-729.


    B. H. Haak, M. Haase and P. C. Kunstmann, Perturbation, interpolation, and maximal regularity, Adv. Differential Equations, 11 (2006), 201-240.


    J. L. Lions and J. Peetre, Sur une classe d'espaces d'interpolation, Inst. Hautes Études Sci. Publ. Math., 19 (1964), 5-68.


    A. Lunardi, "Analytic Semigroups and Optimal Regularity in Parabolic Problems," Birkhaüser Verlag, Basel, 1995.


    E. Sinestrari, On the abstract Cauchy problem of parabolic type in spaces of continuous functions, J. Math. Anal. Appl., 107 (1985), 16-66.doi: 10.1016/0022-247X(85)90353-1.


    H. Triebel, "Interpolation Theory, Functions Spaces, Differential Operators," North-Holland Publishing Co., Amsterdam, New York, 1978.

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