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This work is concerned with the equilibrium configurations of elastic structures
in contact with Coulomb friction. We obtain a variational formulation of this
equilibrium problem. Then we propose sufficient conditions for the existence of
an infinity of equilibrium configurations with arbitrary small friction
coefficients. We illustrate the result in two space dimensions with a
simple example.
In the present paper, we prove the existence and uniqueness of weak solution to a class of nonlinear degenerate elliptic $p$-Laplacian problem with Dirichlet-type boundary condition, the main tool used here is the variational method combined with the theory of weighted Sobolev spaces.
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