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Second order abstract differential equations of elliptic type set in R+

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Języki publikacji
EN
Abstrakty
EN
In this paper we give some new results on complete abstract second order differential equations of elliptic type set in R+. In the framework of UMD spaces, we use the celebrated Dore-Venni Theorem to prove existence and uniqueness for the strict solution. We will use also the Da Prato-Grisvard Sum Theory to furnish results when the space is not supposed to be a UMD space.
Wydawca
Rocznik
Strony
709--727
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
  • Laboratoire de Mathématiques, U.F.R. Sciences et Techniques, Université du Havre, B.P. 540, 76058 Le Havre Cedex, France
autor
  • Laboratoire de Mathématiques, U.F.R. Sciences et Techniques, Université du Havre, B.P. 540, 76058 Le Havre Cedex, France
Bibliografia
  • [1] C. J. K. Batty, R. Chill, S. Srivastava, Maximal regularity for second order non-autonomous Cauchy problems, Studia Math. 189 (2008), 205–223.
  • [2] J. Bourgain, Some remarks on Banach spaces in which martingale difference sequences are unconditional, Ark. Mat. 21 (1983), 163–168.
  • [3] D. L. Burkholder, A geometrical characterisation of Banach spaces in which martingale difference sequences are unconditional, Ann. Probab. 9 (1981), 997–1011.
  • [4] R. Chill, S. Srivastava, Lp-maximal regularity for second order Cauchy problems, Math. Z. 251 (2005), 751–781.
  • [5] G. Da Prato, P. Grisvard, Sommes d’opérateurs linéaires et équations différentielles opérationnelles, J. Math. Pures Appl. 54(9) (1975), 305–387.
  • [6] G. Dore, Lp Regularity for Abstract Differential Equations, Functional Analysis and Related Topics, Kyoto, 1991, Lecture Notes in Math., vol. 1540, Springer-Verlag, Berlin, 1993, pp. 25–38.
  • [7] G. Dore, A. Venni, On the closedness of the sum of two closed operators, Math. Z. 196 (1987), 270–286.
  • [8] A. El Haial, R. Labbas, On the ellipticity and solvability of abstract second-order differential equation, Electron. J. Differential Equations 57 (2001), 1–18.
  • [9] A. Favini, Parabolicity of second order differential equations in Hilbert space, Semigroup Forum 42 (1991), 303–331.
  • [10] A. Favini, R. Labbas, S. Maingot, H. Tanabe, A. Yagi, On the solvability and the maximal regularity of complete abstract differential equations of elliptic type, Funkcial. Ekvac. 47 (2004), 423–452.
  • [11] A. Favini, R. Labbas, S. Maingot, H. Tanabe, A. Yagi, Etude unifiée de problèmes elliptiques dans le cadre höldérien, C. R. Math. Acad. Sci. Paris 341 (2005), 485–490.
  • [12] A. Favini, R. Labbas, H. Tanabe, A. Yagi, On the solvability of complete abstract differential equations of elliptic type, Funkcial. Ekvac. 47 (2004), 205–224.
  • [13] A. Favini, R. Labbas, S. Maingot, H. Tanabe, A. Yagi, Complete abstract differential equations of elliptic type in UMD spaces, Funkcial. Ekvac. 49 (2006), 193–214.
  • [14] A. Favini, R. Labbas, S. Maingot, H. Tanabe, A. Yagi, A simplified approach in the study of elliptic differential equations in UMD spaces and new applications, Funkcial. Ekvac. 51 (2008), 165–187.
  • [15] A. Favini, R. Labbas, S. Maingot, H. Tanabe, A. Yagi, Necessary and sufficient conditions for maximal regularity in the study of elliptic differential equations in Hölder spaces, Discrete Contin. Dyn. Syst. 22(4) (2008), 973–987.
  • [16] J. Liang, T. Xiao, Wellposedness results for certain classes of higher order abstract Cauchy problems connected with integrated semigroups, Semigroup Forum 56 (1998), 84–103.
  • [17] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, Berlin, Heidelberg, Tokyo, 1983.
  • [18] J. Prüss, Maximal regularity for abstract parabolic problems with inhomogeneous boundary data in Lp-spaces, Math. Bohem. 2 (2002), 311–327.
  • [19] J. Prüss, H. Sohr, On operators with bounded imaginary powers in Banach spaces, Math. Z. 203 (1990), 429–452.
  • [20] J. Prüss, H. Sohr, Boundedness of imaginary powers of second-order elliptic differential operators in Lp, Hiroshima Math. J. 23 (1993), 161–192.
  • [21] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, North Holland, Amsterdam, 1978.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-72f58765-3041-4fb5-9f89-832c41749067
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