Geodesic
New results on complete elliptic equations with Robin boundary coefficient-operator conditions in non commutative case
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 1, pp. 70-96

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In this paper, we prove some new results on operational second order differential 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 differential equations; Robin boundary conditions in non commutative cases; analytic semigroup; maximal regularity. 
@article{VYURU_2017_10_1_a4,
     author = {M. Cheggag and A. Favini and R. Labbas and S. Maingot and Kh. Ould Melha},
     title = {New results on complete elliptic equations with {Robin} boundary coefficient-operator conditions in non commutative case},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {70--96},
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     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2017_10_1_a4/}
}
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M. Cheggag; A. Favini; R. Labbas; S. Maingot; Kh. Ould Melha. New results on complete elliptic equations with Robin boundary coefficient-operator conditions in non commutative case. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 10 (2017) no. 1, pp. 70-96. http://geodesic.mathdoc.fr/item/VYURU_2017_10_1_a4/