Abstract
The mathematical model of the flow of a viscous lubricant between elastic bearings leads to the study of a highly non-linear and non-local elliptic variational inequality. We discuss the existence of a solution by using an a prioriL∞-estimate. This method allows us to solve a large class of problems, including those arising from the linear Hertzian theory, and yields new existence results for the cases of a pressure-dependent viscosity or the inclusion of a load constraint. For small data the uniqueness of the solution holds, and we show that in the cylindrical journal bearing problem with small eccentricity ratio, the free boundary is given by two disjoint differentiable arcs close to the free boundary of the first-order approximate solution.
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