We study the regularity of solutions of the obstacle problem when the obstacle is smooth on each half of the unit ball but only Lipschitz across the shared boundary. We prove that the optimal regularity of these solutions is C 1 2 up to the shared boundary on each half of the unit ball. The proof uses a modification of Almgren’s frequency formula.

Gait variability may serve as a sensitive and clinically relevant parameter to quantify adjustments in walking and the changes with aging and neurological disease. Variability of steps preceding obstacle avoidance (approach phase) are important for efficiency in the task, especially in people with Parkinson's disease (PD). However, variability of gait during the approach phase to obstacle avoid...

In the current study, non-Newtonian flow pattern and heat transfer in an enclosure containing a tilted square are examined. In order to numerically simulate the problem, the mesoscopic lattice Boltzmann method is utilized. The non-Newtonian Carreau-Yasuda model is employed. It is able to adequately handle the shear-thinning case. The simulation results of flow and heat transfer have been ...

We study 22 systems of variational inequalities which are only weakly elliptic; in particular, these systems are not necessarily monotone. The prototype diierential operator is the (vector-valued) p-Laplacian. We prove, under certain conditions, the existence of solutions to the unilateral obstacle problem. In addition, we address the question of determining function spaces on which the p-Lapla...

A level set method is proposed for solving free boundary problems coming from contact with obstacles. Two different approaches are described and applied for solving an unilateral obstacle problem. The cost functionals coming from the new approach are nonsmooth. For solving the nonsmooth minimization problems, two methods are applied: firstly, a proximal bundle method, which is a method for solv...