Appl Math Optim 42:169–202 (2000)
2000 Springer-Verlag New York Inc.
Existence Results for Quasistatic Contact Problems
with Coulomb Friction
Department of Mathematics, Link¨oping University,
SE-581 83 Link¨oping, Sweden
Communicated by D. Kinderlehrer
Abstract. We prove the existence of a solution for an elastic frictional, quasistatic,
contact problem with a Signorini non-penetration condition and a local Coulomb
friction law. The problem is formulated as a time-dependent variational problem
and is solved by the aid of an established shifting technique used to obtain increased
regularity at the contact surface. The analysis is carried out by the aid of auxiliary
problems involving regularized friction terms and a so-called normal compliance
Key Words. Coulomb friction, Local friction law, Regularization, Penalization,
Normal compliance unilateral contact, Linear elasticity, Shifting, Variational in-
equalities, Quasistatic, Existence.
AMS Classiﬁcation. 35K85, 49A29.
The main aim of this article is to settle the question of the existence of a solution for
a quasistatic frictional contact problem, which has been open since the early seventies.
We consider an elastic body which occupies a region and may come into contact
with a rigid obstacle along a part S
of its boundary ∂, where we use the so-called
This work was supported by the Swedish Research Council for Engineering Sciences under Contract