The paper deals with solutions of transonic potential flow problems handled in the weak form or as variational inequalities. Using suitable generalized methods, which are well known for elliptic partial differential equations of the second order, some properties of these solutions are derived. A maximum principle, a comparison principle and some conclusions from both ones can be established.
We prove in this paper the Hölder regularity of Almgren minimal sets of dimension 3 in around a -point and the existence of a point of particular type of a Mumford-Shah minimal set in , which is very close to a . This will give a local description of minimal sets of dimension 3 in around a singular point and a property of Mumford-Shah minimal sets in .
In this paper we describe some recent progress on the theory of sets of finite perimeter, currents, and rectifiability in metric spaces. We discuss the relation between intrinsic and extrinsic theories for rectifiability
The purpose of this paper is to make a brief review of results obtained in the theory of variational inequalities for nonclassical operators, namely, of degenerate hyperbolic and variable type.
The minimization of a nonlinear function with linear and nonlinear constraints and simple bounds can be performed by minimizing an augmented Lagrangian function, including only the nonlinear constraints. This procedure is particularly interesting in case that the linear constraints are flow conservation equations, as there exist efficient techniques to solve nonlinear network problems. It is then necessary to estimate their multipliers, and variable reduction techniques can be used to carry out...
In the present work, divided in three parts, one considers a real skis-skier system, , descending along a straight-line with constant dry friction; and one schematizes it by a holonomic system , having any number of degrees of freedom and subjected to (non-ideal) constraints, partly one-sided. Thus, e.g., jumps and also «steps made with sliding skis» can be schematized by . Among the Lagrangian coordinates for two are the Cartesian coordinates and of its center of mass, , relative...