Construction of a bipotential for a multivalued constitutive law

Bipotentials are non smooth mechanics tools, which allows modelling various non associative multivalued constitutive laws of dissipative materials (friction contact, soils, cyclic plasticity of metals, damage). We answer the following question: given a graph M representing a material behaviour, is there a bipotential b for which M is the set of (x, y) such that b (x, y) = 〈x, y 〉? We state a simple necessary and sufficient condition for the existence of b. If it is fulfilled, we construct the bipotential. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An integrated model for logistics network design

In this paper we introduce a new formulation of the logistics network design problem encountered in deterministic, single-country, single-period contexts. Our formulation is flexible and integrates location and capacity choices for plants and warehouses with supplier and transportation mode selection, product range assignment and product flows. We next describe two approaches for solving the problem---a simplex-based branch-and-bound and a Benders decomposition approach. We then propose valid inequalities to strengthen the LP relaxation of the model and improve both algorithms. The computational experiments we conducted on realistic randomly generated data sets show that Benders decomposition is somewhat more advantageous on the more difficult problems. They also highlight the considerable performance improvement that the valid inequalities produce in both solution methods. Furthermore, when these constraints are incorporated in the Benders decomposition algorithm, this offers outstanding reoptimization capabilities.     

Large time behavior of solutions to degenerate parabolic equations with weights

We study the degenerate parabolic equation t_∂u=a(δ(x))upΔu−g(u) in Ω×(0,∞), where Ω⊂RN (N?1) is a smooth bounded domain, p?1, δ(x)=dist(x,∂Ω) and a is a continuous nondecreasing function such that a(0)=0. Under some suitable assumptions on a and g we prove the existence and the uniqueness of a classical solution and we study its asymptotic behavior as t→∞.     

A classification for 2-isometries of noncommutativeLp-spaces

In this paper we extend previous results of Banach, Lamperti and Yeadon on isometries ofL _p-spaces to the non-tracial case first introduced by Haagerup. Specifically, we use operator space techniques and an extrapolation argument to prove that every 2-isometryT:L _p(M) →L _p(N) between arbitrary noncommutativeL _p-spaces can always be written in the form Here π is a normal *-isomorphism fromM onto the von Neumann subalgebra π(M) ofN,w is a partial isometry inN, andE is a normal conditional expectation fromN onto π(M). As a consequence of this, any 2-isometry is automatically a complete isometry and has completely contractively complemented range. The first and second authors were partially supported by the National Science Foundation DMS-0088928 and DMS-0140067.     

On a class of sublinear singular elliptic problems with convection term

We establish several results related to existence, nonexistence or bifurcation of positive solutions for the boundary value problem −Δu+K(x)g(u)+a|∇u|=λf(x,u) in Ω, u=0 on ∂Ω, where Ω⊂RN(N?2) is a smooth bounded domain, 0<a?2, λ is a positive parameter, and f is smooth and has a sublinear growth. The main feature of this paper consists in the presence of the singular nonlinearity g combined with the convection term a|∇u|. Our approach takes into account both the sign of the potential K and the decay rate around the origin of the singular nonlinearity g. The proofs are based on various techniques related to the maximum principle for elliptic equations.     

Embedding of the operator space OH and the logarithmic ‘little Grothendieck inequality’

We use Voiculescu’s concept of free probability to construct a completely isomorphic embedding of the operator space OH in the predual of a von Neumann algebra. We analyze the properties of this embedding and determine the operator space projection constant of OH_n:

Positive Harmonic Functions that Vanish on a Subset of a Cylindrical Surface

This paper investigates positive harmonic functions on domains that are complementary to a subset of a cylindrical surface. It characterizes, both in terms of harmonic measure and of a Wiener-type criterion, those domains that admit minimal harmonic functions with exponential growth. Illustrative examples are provided. Two applications are also given. The first of these concerns minimal harmonic functions associated with an irregular boundary point, and amplifies a recent construction of Gardiner and Hansen. The second concerns the possible non-approximability of positive harmonic functions by integrable positive harmonic functions. This research was supported by Science Foundation Ireland under Grant 06/RFP/MAT057, and is also part of the programme of the ESF Network “Harmonic and Complex Analysis and Applications” (HCAA).     

Lipschitz Domains,Domains with Corners,and the Hodge Laplacian

ABSTRACT

We define self-adjoint extensions of the Hodge Laplacian on Lipschitz domains in Riemannian manifolds, corresponding to either the absolute or the relative boundary condition, and examine regularity properties of these operators' domains and form domains. We obtain results valid for general Lipschitz domains, and stronger results for a special class of “almost convex” domains, which apply to domains with corners.     

Global Unique Solvability of Inhomogeneous Navier-Stokes Equations with Bounded Density

In this paper, we prove the global existence and uniqueness of solution to d-dimensional (for d = 2, 3) incompressible inhomogeneous Navier-Stokes equations with initial density being bounded from above and below by some positive constants, and with initial velocity u₀ ∈ H^s( R ²) for s > 0 in 2-D, or u₀ ∈ H¹( R ³) satisfying ‖u₀‖_L² ‖?u₀‖_L² being sufficiently small in 3-D. This in particular improves the most recent well-posedness result in [10 Danchin , R. , Mucha , P.B. ( 2013 ). Incompressible flows with piecewise constant density . Arch. Rat. Mech. Anal. 207 : 991 – 1023 .[Crossref], [Web of Science ®] , [Google Scholar]], which requires the initial velocity u₀ ∈ H²( R ^d) for the local well-posedness result, and a smallness condition on the fluctuation of the initial density for the global well-posedness result.