Relations Between Certain Abstract Sobolev Problems and an Associated Euler-Poisson-Darboux Problems

Abstract

AMS (MOS): 35Q20, 34G10

Let X be a Banach space and let B be the generator of a continuous group in X such that A = B² generates an equibounded semi-group. Let C generate a continuous group in X or else generate an equibounded semi-group in X . If A · C = C · A and if ⊘,f(t) are members of an appropriate dense domain of X , it is shown that the solution of the Sobolev problem

can be expressed as an appropriate transform of a solution of

A second order version of the above Sobolev equation is also considered.

¹This research was supported by an Oakland University Research Fellowship

¹This research was supported by an Oakland University Research Fellowship

Notes

¹This research was supported by an Oakland University Research Fellowship

Additional information

Notes on contributors

R. Carroll

L. R. Bragg