Papers by Mustapha CHEGGAG
Bulletin of the South Ural State University. Series "Mathematical Modelling, Programming and Computer Software", 2017
In this paper, we prove some new results on operational second order dierential equations of elli... more In this paper, we prove some new results on operational second order dierential equations of elliptic type with general Robin boundary conditions in a non-commutative framework. The study is performed when the second member belongs to a Sobolev space. Existence, uniqueness and optimal regularity of the classical solution are proved using interpolation theory and results on the class of operators with bounded imaginary powers. We also give an example to which our theory applies. This paper improves naturally the ones studied in the commutative case by M. Cheggag, A. Favini, R. Labbas, S. Maingot and A. Medeghri: in fact, introducing some operational commutator, we generalize the representation formula of the solution given in the commutative case and prove that this representation has the desired regularity. Keywords: second-order elliptic dierential equations; Robin boundary conditions in non commutative cases; analytic semigroup; maximal regularity. Dedicated to Professor Angelo Favini on his 70th birthday.
Sturm-Liouville problems for an abstract differential equation of elliptic type in UMD spaces
Differential and Integral Equations
ABSTRACT In this paper we give some new results on Sturm-Liouville abstract problems of second-or... more ABSTRACT In this paper we give some new results on Sturm-Liouville abstract problems of second-order differential equations of elliptic type in UMD spaces. Existence, uniqueness and maximal regularity of the strict solution are proved using the celebrated Dore-Venni theorem. This work completes the problems studied by Favini, Labbas, Maingot, Tanabe and Yagi under Dirichlet boundary conditions, see [6].
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Papers by Mustapha CHEGGAG