Second-Order Differential Operators with Non-Local Ventcel's Boundary Conditions

Abstract

Different boundary conditions have been introduced for second-order differential operators and the properties of the operators on the corresponding domains have been deeply investigated since the work of Feller. The aim of this paper is to study second-order differential operators satisfying a Ventcel's type boundary condition which involves simultaneously both the endpoints of a real interval. We study different general properties and a resolvent estimate for this kind of operators.