Boundary value problems for variational integrals involving surface curvatures
Boundary value problems for variational integrals involving surface curvatures
The following investigation deals with surfaces governed by and extremal for a free energy functional which is quadratic in the principal curvatures. The associated Euler-Lagrange differential equations are derived, as are the corresponding intricate natural boundary conditions. Pertinent boundary value problems—without and with volume constraints—are formulated and discussed<inline-formula content-type="math/mathml"> <mml:math …