Mutational equations of the morphological dilation tubes

The present paper provides some differential results dealing with the morphological dilation of a compact set in the nonregular case. Indeed the evolution of dilated sets with respect to time is characterized through mutational equations which are new mathematical tools extending the concept of differential equations to the metric space of all nonempty compact sets of ⁿ . Using this new tool, we prove that the mutation of the dilation is the normal cone which is a generalization of the classical notion of normal. This result clearly establishes that the dilation transforms this initial set in the direction of the normal at any point of the set. Furthermore, it does not require any regularity assumptions on the compact set.