A class of nonlinear variational problems appearing in the theory of magnetoelasticity of thin superconducting shells
Ari Arievich Laptev, Michael Levitin, D. G. Vasil'ev · Nonlinearity · 1991
The authors consider the variational problem describing the static deformation of a thin elastic superconducting shell in a magnetic field; the shell is supposed to be clamped along the edge. This problem is essentially nonlinear because the functional in the problem depends on the unknown deformed shell middle surface. For sufficiently weak fields and under some additional simplifications they prove that the solution of this problem exists and is unique.