Derivation and application of a novel integral inequality

A new vector volume integral inequality has been derived using calculus of variations techniques [1]. This inequality was used to determine conditions for waveguide cutoff. The use of the inequality requires only the knowledge of the smallest eigenvalue of the vector Helmholtz´s equation for the geometry of the waveguide. The inequality can also be of value in applications of Liapunov Stability Theory to systems of partial differential equations. This result is illustrated by an example.