Some properties of the solutions of obstacle problems with measure data

We study some properties of the obstacle reactions associated with the solutions of unilateral obstacle problems with measure data. These results allow us to prove that, under very weak assumptions on the obstacles, the solutions do not depend on the components of the negative parts of the data which are concentrated on sets of capacity zero. The proof is based on a careful analysis of the behaviour of the potentials of two mutually singular measures near the points where both potentials tend to infinity.Comment: 18 page

Uniqueness of solutions to Hamilton-Jacobi equations arising in the Calculus of Variations

We prove the uniqueness of the viscosity solution to the Hamilton-Jacobi equation associated with a Bolza problem of the Calculus of Variations, assuming that the Lagrangian is autonomous, continuous, superlinear, and satisfies the usual convexity hypothesis. Under the same assumptions we prove also the uniqueness, in a class of lower semicontinuous functions, of a slightly different notion of solution, where classical derivatives are replaced only by subdifferentials. These results follow from a new comparison theorem for lower semicontinuous viscosity supersolutions of the Hamilton-Jacobi equation, that is proved in the general case of lower semicontinuous Lagrangians.Comment: 14 page

Boundary Asymptotic Analysis for an Incompressible Viscous Flow: Navier Wall Laws

We consider a new way of establishing Navier wall laws. Considering a bounded domain $\Omega$ of R N , N=2,3, surrounded by a thin layer $\Sigma \epsilon$, along a part $\Gamma$2 of its boundary $\partial \Omega$, we consider a Navier-Stokes flow in $\Omega \cup \partial \Omega \cup \Sigma \epsilon$ with Reynolds' number of order 1/$\epsilon$ in $\Sigma \epsilon$. Using $\Gamma$-convergence arguments, we describe the asymptotic behaviour of the solution of this problem and get a general Navier law involving a matrix of Borel measures having the same support contained in the interface $\Gamma$2. We then consider two special cases where we characterize this matrix of measures. As a further application, we consider an optimal control problem within this context

Past and present financialization in Central Eastern Europe: the case of Western subsidiary banks

By examining the ‘post’ financial crisis scenario in Central Eastern Europe (CEE) the paper assesses the role of Western banks in the region and how their penetration and ‘resilience’ is influenced by their parent and subsidiary structure. While taking stock of the variegated post-socialist transformation in CEE, it employs a genealogical method to explore how the universal bank model and its current ‘bifurcation’ into parent and subsidiary bank provides a lens through which to investigate a new form of dependency within the uneven geography of Europe. In the light of Rudolf Hilferding’s theory of the universal bank and the theorization of financial capital, it illustrates how the present form of bank capitalization overlaps with previous forms of imperial expansion. If on one hand subsidiaries sit at the intersection between the core (home country) and the periphery (host country)— reproducing some of the old spatial hierarchy of capitalism; on the other they also enable new patterns of value extraction that go beyond these relations of dependency. Their autonomy in raising capital and in responding to local host jurisdiction in their “second home market” opens a new financial dimension of extractions that escape the oversight of national and regional regulatory regimes

A model for the quasi-static growth of brittle fractures based on local minimization

We study a variant of the variational model for the quasi-static growth of brittle fractures proposed by Francfort and Marigo. The main feature of our model is that, in the discrete-time formulation, in each step we do not consider absolute minimizers of the energy, but, in a sense, we look for local minimizers which are sufficiently close to the approximate solution obtained in the previous step. This is done by introducing in the variational problem an additional term which penalizes the $L^2$-distance between the approximate solutions at two consecutive times. We study the continuous-time version of this model, obtained by passing to the limit as the time step tends to zero, and show that it satisfies (for almost every time) some minimality conditions which are slightly different from those considered in Francfort and Marigo and in our previous paper, but are still enough to prove (under suitable regularity assumptions on the crack path) that the classical Griffith's criterion holds at the crack tips. We prove also that, if no initial crack is present and if the data of the problem are sufficiently smooth, no crack will develop in this model, provided the penalization term is large enough.Comment: 20 page

Quasistatic crack growth in elasto-plastic materials with hardening: The antiplane case

We study a variational model for crack growth in elasto-plastic materials with hardening in the antiplane case. The main result is the existence of a solution to the initial value problem with prescribed time-dependent boundary conditions

Validity and failure of the integral representation of Γ-limits of convex non-local functionals

We prove an integral-representation result for limits of non-local quadratic forms on H-0(1)(Omega), with Omega a bounded open subset of R-d, extending the representation on C-c(infinity)(Omega) given by the Beurling Deny formula in the theory of Dirichletforms. We give a counter example showing that a corresponding representation may not hold if we consider analogous functionals in W-0(1,p)(Omega), with p not equal 2and 1 < p <=

A new space of generalised functions with bounded variation motivated by fracture mechanics

We introduce a new space of generalised functions with bounded variation to prove the existence of a solution to a minimum problem that arises in the variational approach to fracture mechanics in elastoplastic materials. We study the fine properties of the functions belonging to this space and prove a compactness result. In order to use the Direct Method of the Calculus of Variations we prove a lower semicontinuity result for the functional occurring in this minimum problem. Moreover, we adapt a nontrivial argument introduced by Friedrich to show that every minimizing sequence can be modified to obtain a new minimizing sequence that satisfies the hypotheses of our compactness result