We prove that the obstacle problem for a non-uniformly parabolic operator of Kolmogorov type, with Cauchy (or Cauchy-Dirichlet) boundary conditions, has a unique strong solution u. We also show that u is a solution in the viscosity sense.

We study the penalized obstacle problem in the unit half ball, i.e. an approximation of the obstacle problem in the unit half ball. The main result states that when the approximation parameter is small enough and when certain level sets are sufficiently close to the hyperplane {x1 = 0}, then these level sets are uniformly C1 regular graphs. As a by-product, we also recover some regularity of th...

Abstract: We prove an existence and uniqueness result for quasilinear Stochastic PDEs with obstacle (OSPDE in short). Our method is based on analytical technics coming from the parabolic potential theory. The solution is expressed as a pair (u, ν) where u is a predictable continuous process which takes values in a proper Sobolev space and ν is a random regular measure satisfying minimal Skohoro...

Results. Using an attentional allocation index (AAI) to compare performance of healthy young and older adults and to measure the flexibility of allocation of attention, results showed a tendency in older adults toward a decreased ability to flexibly allocate their attention between the two tasks, with small AAI values. The decreased ability to allocate attention in older adults was found to be ...

In this paper we proposed a modified Lagrangian functional for obstacle problem, investigated its properties. Then we construct Uzawa method for finding a saddle point, proved the convergence theorems. Some numerical examples are provided.

This paper deals with nonholonomic motion planning including obstacle avoidance capabilities. We show that the methods developed in absence of obstacles can be extended to the problem of obstacle avoidance, provided that they verify a topological property. Such steering methods allow us to design exact and complete collision-free path planners for a large family of systems. We show that the ste...

Dans une permutation, un record est maximum ou minimum, en partant de la droite gauche. Les éléments d’une permutation peuvent être classés deux types : les records (dits points extérieurs) et autres intérieurs). permutations sans point intérieur ont été étudiées sous le nom carrées. Ici, nous explorons ayant nombre fini intérieurs, dites quasi-carrées. Contrairement aux carrées, l’énumération ...