Solution to the stationary problem of glacier dynamics

A stationary problem of the non-Newtonian fluid dynamics is applied to the modeling of an alpine glacier motion with Dirichlet boundary conditions corresponding to the ice increment in the upper part of the glacier and to the ice meltdown in its lower part. The existence of a weak solution in a functional class with the first-order derivatives integrable to the power $q>6/5$ is established for sufficiently small given boundary data. The proof is largely based on regularizing weak solutions and using properties of monotone operators.