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

Abstract

Different boundary conditions have been introduced for second-order differential operators and theproperties of the operators on the corresponding domains have been deeply investigated since the work of Feller. Theaim of this paper is to study second-order differential operators satisfying a Ventcel’s type boundary condition whichinvolves simultaneously both the endpoints of a real interval. We study different general properties and a resolventestimate for this kind of operators.