Summary
This paper considers the problems of minimizing Gateaux-differentiable functionals over subsets of real Banach spaces defined by a non-linear equality constraint. The existence of a Lagrange multiplier is proved, together with approximation results on the constrained subset, provided a nonlinear compatibility condition, generalizing the classical inf-sup condition, is satisfied. These ideas are applied to equilibrium problems in incompressible finite elasticity and lead to convergence results for these problems.
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Le Tallec, P. Existence and approximation results for nonlinear mixed problems: Application to incompressible finite elasticity. Numer. Math. 38, 365–382 (1982). https://doi.org/10.1007/BF01396438
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DOI: https://doi.org/10.1007/BF01396438