Second Order Abstract Differential Equations of Elliptic Type Set in R+,
Abstract
In this paper we give some new results on complete abstract second order differential equations of elliptic type set in R₊. In the framework of UMD spaces, we use the celebrated Dore-Venni Theorem to prove existence and uniqueness for the strict solution. We will use also the Da Prato-Grisvard Sum Theory to furnish results when the space is not supposed to be a UMD space.
Keywords
Abstract differential equations of second order
Boundary conditions
UMD spaces
Bounded imaginary powers
Maximal regularity
Dore-Venni theorem
Da Prato-Grisvard Sum Theory
''Abstract differential equations of second order''
''Boundary conditions''
''UMD spaces''
''Bounded imaginary powers''
'' Maximal regularity''
''Dore-Venni theorem''
''Da Prato-Grisvard Sum Theory.''