Geodesic
Robin boundary value problems for elliptic operational differential equations with variable coefficients
Electronic Journal of Differential Equations, Tome 2015 (2015).

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Summary: In this article we give some new results on abstract second-order differential equations of elliptic type with variable operator coefficients and general Robin boundary conditions, in the framework of Holder spaces. We assume that the family of variable coefficients verify the well known Labbas-Terreni assumption used in the sum theory. We use Dunford calculus, interpolation spaces and the semigroup theory to obtain existence, uniqueness and maximal regularity results for the solution of the problem.
Classification : 34K10, 34K30, 35J25, 35J40, 47A60
Keywords: elliptic equation, Robin boundary conditions, analytic semigroup, maximal regularity, dunford operational calculus 
@article{EJDE_2015__2015__a89,
     author = {Haoua, Rabah and Medeghri, Ahmed},
     title = {Robin boundary value problems for elliptic operational differential equations with variable coefficients},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2015},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a89/}
}
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Haoua, Rabah; Medeghri, Ahmed. Robin boundary value problems for elliptic operational differential equations with variable coefficients. Electronic Journal of Differential Equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a89/