**Avtandil Gachechiladze, Roland Gachechiladze**

##
Unilateral Contact Problems for Homogeneous Hemitropic Elastic Solids with a
Friction

**abstract:**

In the present paper, we study a one-sided contact problem for a micropolar
homogeneous elastic hemitropic medium with a friction. Here, on a part of the
elastic medium surface with a friction, instead of a normal component of force
stress there is prescribed the normal component of the displacement vector. We
consider two cases, the so-called coercive case (when the elastic medium is
fixed along some part of the boundary) and noncoercive case (without fixed
parts). By using the Steklov-Poincaré
operator, we reduce this problem to an equivalent boundary variational
inequality. Based on our variational inequality approach, we prove the existence
and uniqueness theorems for the weak solution. In the coercive case, the problem
is unconditionally solvable, and the solution depends continuously on the data
of the original problem. In the noncoercive case, we present in a closed-form
the necessary condition for the existence of a solution of the contact problem.
Under additional assumptions, this condition is also sufficient for the
existence of a solution.

**Mathematics Subject Classification:**
35J86, 49J40, 74M10, 74M15

**Key words and phrases:** Elasticity theory, hemitropic solids, contact
problem with a friction, boundary variational inequality