Solvability of the steady-state problem of the movement of a mountain glacier.

We consider a steady-state problem of non-Newtonian fluid dynamics that models the movement of mountain glaciers. We specify Dirichlet boundary conditions corresponding to the ice accumulation in the upper part of the glacier and to the ice meltdown in the lower part. We prove the existence of a generalized solution of the problem in the class of functions with first-order derivatives integrable to the power q>6/5 for a sufficiently small velocity field specified on the boundary. The proof is based mainly on the regularization of the generalized solutions and the properties of monotone operators.