Geodesic
Elliptic problems with Robin boundary coefficient-operator conditions in general $L_p$ Sobolev spaces and applications
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 3, pp. 56-77

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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 $L^{p}(0,1; X)$ with general $p\in (1,+\infty)$, $X$ 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.
Keywords: second-order abstract elliptic differential equations; Robin boundary conditions; analytic semigroup. 
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     author = {M. Cheggag and A. Favini and R. Labbas and S. Maingot and A. Medeghri},
     title = {Elliptic problems with {Robin} boundary coefficient-operator conditions in general $L_p$ {Sobolev} spaces and applications},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {56--77},
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M. Cheggag; A. Favini; R. Labbas; S. Maingot; A. Medeghri. Elliptic problems with Robin boundary coefficient-operator conditions in general $L_p$ Sobolev spaces and applications. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 3, pp. 56-77. http://geodesic.mathdoc.fr/item/VYURU_2015_8_3_a3/