ÉTUDE DE PROBLÈMES DE TRANSMISSION RÉGIS PAR DES ÉQUATIONS DIFFÉRENTIELLES ABSTRAITES DE TYPE ELLIPTIQUE - Kheira LIMAM (My University, 2012)
This thesis is devoted essentially to study, in two frameworks, the existence, uniqueness and maximal regularity of the solutions of a family of transmission problems governed by an abstract second order di¤erential equations with Robin boundary conditions. In the rst framework (Lp spaces), we treated two transmission problems, under certain assumptions on the operators (ellipticity, Bip, commutativity) and on the space (UMD or not). In the second framework, we studied a transmission problem, set in unbounded domain composed of a half line and a thin layer, under the ellipticity assumption. The right-hand term of the equation is a Hölder continuous function.
Keywords: Abstract di¤erential equations, Transmission problems, Dunford functional cal- culus, Semigroups, UMD spaces, Hölder spaces, Interpolation spaces, Bounded imaginary powers (Bip), Theory of the sum of operators, Thin layer, Strict solution, Maximal regula- rity.