Abstract
The Young-Laplace relation states that the interface separating two fluids, develops in such a way that the difference between the outer and the inner pressure remains proportional to the mean curvature at every point of the interface. This relation guides the evolution of a free boundary. Considering the importance of the ellipsoidal surfaces as free boundaries in anisotropic evolutions, it is of great interest to have ready-to-use formulae for the mean curvature of a perturbed ellipsoidal surface. These formulae provide the basis for the stability analysis of free boundary value problems in Fluid Mechanics. The present work calculates the first order approximation of the local curvatures for a surface which is a perturbation of an ellipsoid.
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