Sensitivity analysis of a Tresca-type problem leads to Signorini's conditions

The present paper investigates the sensitivity analysis, with respect to right-hand source term perturbations, of a scalar Tresca-type problem. This simplified, but nontrivial, model is inspired from (vectorial) Tresca friction problem found in contact mechanics. weak formulation considered leads variational inequality second kind depending on perturbation parameter. unique solution this then characterized by using proximal operator corresponding nondifferentiable convex integral functional. We compute subdifferential functional Sobolev space H^1(Omega) and show that all its subgradients satisfy PDE boundary condition involving integrand. With aid twice epi-differentiability, concept introduced thoroughly studied R.T. Rockafellar, we differentiability parameterized derivative satisfies Signorini-type Some numerical simulations are provided order illustrate our main theoretical result. To best knowledge, first time epi-differentiability applied context mechanical problems, which makes contribution new original literature.