With the advent of modern functional analysis and the theory of distributions it became possible in the early 1950's to systematically explore and develop the theory of partial differential equations (PDE) to a degree previously unimaginable. One important feature of this work was the determination of "natural" spaces of functions of distributions in which to pose various differential problems. Then linear differential operators were treated as abstract linear operators A mapping a domain of definition D(A) C F into G for suitable locally convex topological vector spaces F and G. The abstract operational properties of A were studied and existence-uniqueness theorems for example were then deduced as results in operator theory. This kind of approach was extensively developed also for certain types of nonlinear problems beginning in the early 1960's. In theoretical and applied work in other aspects of PDE one frequently has recourse to these now well established operational methods and distribution techniques. It is no accident that this material interacts naturally with various geometrical and variational points of view for example and enriches studies i n these contexts. Much of this material already appears in book form but research continues and we will report on some recent work as indicated below.
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