A Function Theoretic Approach to Higher Order Pseudoparabolic Equations

Bhatnagar and Gilbert developed an analytic theory for pseudoparabolic equations in three space variables. In this paper the authors continue this approach for this class of equations in four space variables. The authors remark, however, these techniques are only limited up to four space variables. This follows from a theorem due the Kukral who proved that a Bergman-type auxillary variable does not exist for Laplace's equation in more than four variables.