Elliptic problems with Robin boundary coefficient-operator conditions in general Lp Sobolev spaces and applications

Elliptic problems with Robin boundary coefficient-operator conditions in general Lp Sobolev spaces and applications

Автор: Cheggag M., Favini A., Labbas R., Maingot S., Medeghri A.

Журнал: Вестник Южно-Уральского государственного университета. Серия: Математическое моделирование и программирование @vestnik-susu-mmp

Рубрика: Математическое моделирование

Статья в выпуске: 3 т.8, 2015 года.

Бесплатный доступ

In this paper we prove some new results on complete operational second order differential equations of elliptic type with coefficient-operator conditions, in the framework of the space Lp(0,1;X) with general pϵ(1,+∞), X being a UMD Banach space. Existence, uniqueness and optimal regularity of the classical solution are proved. This paper improves and completes naturally our last two works on this problematic.

Second-order abstract elliptic differential equations, robin boundary conditions, analytic semigroup

Короткий адрес: https://sciup.org/147159331

IDR: 147159331   |   DOI: 10.14529/mmp150304

Список литературы Elliptic problems with Robin boundary coefficient-operator conditions in general Lp Sobolev spaces and applications

  • Bourgain J. Some Remarks on Banach Spaces in which Martingale Difference Sequences are Unconditional. Ark. Mat., 1983, vol. 21, pp. 163-168. DOI: DOI: 10.1007/BF02384306
  • Burkholder D.L. A Geometrical Characterisation of Banach Spaces in which Martingale Difference Sequences are Unconditional. Ann. Probab., 1981, vol. 9, pp. 997-1011. DOI: DOI: 10.1214/aop/1176994270
  • Favini A., Labbas R., Maingot S., Tanabe H., Yagi A. Complete Abstract Differential Equations of Elliptic Type in UMD Spaces. Funkcialaj Ekvacioj, 2006, vol. 49, pp. 193-214. DOI: DOI: 10.1619/fesi.49.193
  • Favini A., Labbas R., Maingot S., Tanabe H., Yagi A. A Simplified Approach in the Study of Elliptic Differential Equations in UMD Spaces and New Applications. Funkcialaj Ekvacioj, 2008, vol. 51, pp. 165-187. DOI: DOI: 10.1619/fesi.51.165
  • El Haial A., Labbas R. On the Ellipticity and Solvability of Abstract Second-Order Differential Equation. Electronic Journal of Differential Equations, 2001, vol. 57, pp. 1-18.
  • Favini A., Labbas R., Tanabe H., Yagi A. On the Solvability of Complete Abstract Differential Equations of Elliptic Type. Funkcialaj Ekvacioj, 2004, vol. 47, pp. 205-224.
  • Favini A., Labbas R., Maingot S., Tanabe H., Yagi A. On the Solvability and the Maximal Regularity of Complete Abstract Differential. Equations of Elliptic Type. Funkcialaj Ekvacioj, 2004, vol. 47, pp. 423-452. DOI: DOI: 10.1619/fesi.47.423
  • Favini A., Labbas R., Maingot S., Tanabe H., Yagi A. Etude Unifiée de Problèmes Elliptiques dans le Cadre Höldérien. C.R. Acad. Sci. Paris, Ser. I, 2005, vol. 341, pp. 485-490.
  • Favini A., Labbas R., Maingot S., Tanabe H., Yagi A. Necessary and Sufficient Conditions in the Study of Maximal Regularity of Elliptic Differential Equations in Holder Spaces. Discrete and Continuous Dynamical Systems, 2008, vol. 22, pp. 973-987. DOI: DOI: 10.3934/dcds.2008.22.973
  • Cheggag M., Favini A., Labbas R., Maingot S., Medeghri A. Abstract Differential Equations of Elliptic Type with General Robin Boundary Conditions in Hölder Spaces. Applicable Analysis, 2012, vol. 91, no. 8, pp. 1453-1475. DOI: DOI: 10.1080/00036811.2011.635653
  • Cheggag M., Favini A., Labbas R., Maingot S., Medeghri A. Sturm -Liouville Problems for an Abstract Differential Equation of Elliptic Type in UMD Spaces. Differential and Integral Equations, 2008, vol. 21, no. 9-10, pp. 981-1000.
  • Cheggag M., Favini A., Labbas R., Maingot S., Medeghri A. Complete Abstract Differential Equations of Elliptic Type with General Robin Boundary Conditions in UMD Spaces. Discrete and Continuous Dynamical Systems -Series S, 2011, vol. 4, no. 3, pp. 1-16.
  • Dore G., Venni A. On the Closedness of the Sum of Two Closed Operators. Mathematicsche zeitschrift, 1987, vol. 196, pp. 124-136. DOI: DOI: 10.1007/BF01163654
  • Prüss J., Sohr H. On Operators with Bounded Imaginary Powers in Banach Spaces. Mathematicsche zeitschrift, 1990, vol. 203, pp. 429-452. DOI: DOI: 10.1007/BF02570748
  • Lions J.L., Peetre J. Sur Une Classe D'Espaces D'Interpolation. Publications Mathématiques de l'Institut des Hautes Études Scientifiques, 1964, vol. 19, no. 1, pp. 5-68. DOI: DOI: 10.1007/BF02684796
  • Triebel H. Interpolation Theory, Function Spaces, Differential Operators. Amsterdam, North Holland, 1978.
  • Favini A., Labbas R., Maingot S., Meisner M. Boundary Value Problem for Elliptic Differential Equations in Noncommutative Cases. Discrete and Continuous Dynamical Systems, 2013, vol. 33, no. 11-12, pp. 4967-4990.
  • Haase M. The Functional Calculus for Sectorial Operators. Operator Theory: Advances and Applications, 2006, vol. 169, pp. 19-60.
  • Lunardi A. Analytic Semigroups and Optimal Regularity in Parabolic Problems. Birkhäuser, Basel, 1995.
  • Pazy A. Semigroups of Linear Operators and Applications to Partial Differential Equations. Berlin, Heidelberg, Tokyo, Springer-Verlag, 1983.
  • Engel K., Nagel R. One-Parameter Semigroups for Linear Evolution Equtions, New York, Springer Verlag, 2000.
  • Balakrishnan A.V. Fractional Powers of Closed Operators and the Semigroups Generated by Them. Pacific J. Math., 1960, vol. 10, pp. 419-437. DOI: DOI: 10.2140/pjm.1960.10.419
  • Prüss J., Sohr H. Imaginary Powers of Elliptic Second Order Differential Operators in Lp-Spaces. Hiroshima Math. J., 1993, vol. 23, pp. 161-192.
  • Cheggag M., Favini A., Labbas R., Maingot S., Medeghri A. Spectral Parameter Problems with Robin Boundary Coefficient-Operator Conditions in UMD Spaces and Applications. (To appear)
Еще
Статья научная
SciUp 2024 © 2024 ©