Let be some bounded simply connected region in with . We seek a function with values in a Hilbert space which satisfies the equation , where are families of linear operators (possibly unbounded) with everywhere dense domain ( does not depend on ) in and . The values are given in . This problem is not in general well posed in the sense of Hadamard. We give theorems of uniqueness and stability of the solution of the above problem.
"Boundary value problems for second-order partial differential equations with operator coefficients." Abstr. Appl. Anal. 6 (5) 253 - 266, 25 November 2001. https://doi.org/10.1155/S1085337501000628