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

Autores: Angelo Favini, Rabah Labbas, Keddour Lemrabet, Boubaker-Khaled Sadallah
Localización: Revista matemática complutense, ISSN-e 1988-2807, ISSN 1139-1138, Vol. 21, Nº 1, 2008, págs. 89-133
Idioma: inglés
DOI: 10.5209/rev_rema.2008.v21.n1.16438
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Resumen
- 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.