On closability and bounded invertibility of mixed type differential operator in an unbounded domain
Keywords:
operator of mixed type, closure, resolvent, bounded invertibility, inverse operator, unbounded domain, strip, covering, kernel, conjugate operator, Fourier transformAbstract
In this paper we consider a class of mixed type singular differential operator in an unbounded domain. Initially closability of the operator is proved. Because there is no a priori estimate, which exists in the case of an operator whose coefficients depend only on the variable y in front of terms ux (x, y) and u (x, y). The existence of the resolvent of the operator in an unbounded domain is proved. The method of localization and methods of the theory of linear operators are used.
