Partial Differential Equations, Operator Theory and Applications

摘要

The senior investigators on this grant have been active in the following subjects: Cordes has been working on algebras of operators which include partial differential operators as special cases. In particular, he has made detailed investigations of the symbol of a pseudo-differential operator. Kato has concerned himself with problems in scattering theory, its generalizations in functional analysis, and various applications to partial differential equations. He has also obtained results on the nonstationary flow of viscous fluids. Lehman studied extensions of the sloping beach problem and related mixed boundary value problems which arise in electromagnetic diffraction theory. He has also used sophisticated computer techniques to study the first 250,000 zeros of the Riemann zeta-function. Miller has investigated the approximation of solutions of problems in partial differential equations when the data are ill-posed. He has also studied regular and irregular boundary points of solutions of elliptic differential equations. Protter has employed the maximum principle to obtain results on the capacity of conductors and estimates for the spectrum of elliptic operators. He has also studied the relation of difference equations to the functional form of solutions of differential equations. (Author)