Resumen de Study of a complete abstract differential equation of elliptic type variable operator coefficients, I

Angelo Favini, Rabah Labbas, Keddour Lemrabet, Boubaker-Khaled Sadallah

• The aim of this first work is the resolution of an abstract complete second order differential equation of elliptic type with variable operator coefficients set in a small length interval. We obtain existence, uniqueness and maximal regularity results under some appropriate differentiability assumptions combining those of Yagi (1977) and Da Prato-Grisvard (1975). An example for the Laplacian in a regular domain of will illustrate the theory. A forthcoming work (Part II) will complete the present one by the study of the Steklov-Poincaré operator related to this equation when the length of the interval tends to zero.