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Perturbation of nonlinear Dirichlet problems Fournier, David Anthony

Abstract

The solutions of weakly-formulated non-linear Dirichlet problems are studied when the data of the problem are perturbed in various ways. The data which undergo perturbations include the Lagrangian, the boundary condition, the basic domain, and the constraints, if present. The main conclusion states that the solution of the Dirichlet problem which minimizes the Dirichlet integral varies continuously with the data so long as it is unique. Detailed hypotheses are formulated to insure the validity of this conclusion for several large classes of problem. The hypotheses are not much stronger than the standard sufficient conditions for existence, in the generalized Lusternik-Schnirelman theory of these problems.

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