Asymptotic Analysis - Volume 32, issue 3-4

Authors: Imanuvilov, Oleg Yu.

Article Type: Research Article

Abstract: We prove a Carleman inequality for the second order hyperbolic equation in the cylinder Q with the norm of right‐hand side taken in the space (W1 2 (Q))* .

Keywords: Carleman estimate, hyperbolic equation

Citation: Asymptotic Analysis, vol. 32, no. 3-4, pp. 185-220, 2002

Authors: Michel, Laurent

Article Type: Research Article

Abstract: We study the semi‐classical asymptotic as h→0 of the scattering amplitude f(θ,ω,λ,h) associated to a Schrödinger operator H(h)=−½h2 Δ+V(x) for short‐range trapping perturbations. Our main result yields the leading term of the integral of f(θ,ω,λ,h) for θ,ω∈Sn−1 fixed and λ∈[λ0 −ε,λ0 +ε], ε>0, λ0 >0, being a trapping energy level.

Citation: Asymptotic Analysis, vol. 32, no. 3-4, pp. 221-255, 2002

Authors: Bouclet, Jean‐Marc

Article Type: Research Article

Abstract: The main goal of this paper is to introduce tools able to replace Krein's spectral shift function when it cannot be defined. We introduce a function η, for a class of perturbations of pseudodifferential operators on $\mathbb{R}$ d , when these perturbation decay as 〈x〉−ρ , ρ>d/2, at infinity. In Euclidean scattering, we establish a complete asymptotic expansion for η, under the usual nontrapping assumption and we deduce a Levinson formula for the Schrödinger operator on $\mathbb{R}$ 3 . Some results on the general case ρ>0 are also given.

Citation: Asymptotic Analysis, vol. 32, no. 3-4, pp. 257-291, 2002

Authors: Bildhauer, M. | Fuchs, M.

Article Type: Research Article

Abstract: We consider integrands f :$\mathbb{R}$ nN →$\mathbb{R}$ which are of lower (upper) growth rate s≥2 (q>s) and which satisfy an additional structural condition implying the convex hull property, i.e., if the boundary data of a minimizer u :Ω→$\mathbb{R}$ N of the energy ∫Ω f(∇u) dx respect a closed convex set K⊂$\mathbb{R}$ N , then so does u on the whole domain. We show partial C1,α ‐regularity of bounded local minimizers if q<min {s+2/3,sn/(n−2)} and discuss cases in which the latter condition on the exponents can be improved. Moreover, we give examples of integrands which fit into our category …and to which the results of Acerbi and Fusco [2] do not apply, in particular, we give some extensions to the subquadratic case. Show more

Keywords: regularity, minimizers, anisotropic growth

Citation: Asymptotic Analysis, vol. 32, no. 3-4, pp. 293-315, 2002

Authors: Stefanov, Plamen

Article Type: Research Article

Citation: Asymptotic Analysis, vol. 32, no. 3-4, pp. 317-333, 2002

Authors: Hajouj, Brahim | Madaune‐Tort, Monique

Article Type: Research Article

Abstract: In this paper some variational inequalities of second order used in the elasto‐plasticity theory are compared with first order inequalities. Convergence properties in Sobolev spaces are given thanks to a priori estimates and a uniqueness result for first order inequalities.

Citation: Asymptotic Analysis, vol. 32, no. 3-4, pp. 335-358, 2002

Article Type: Other

Citation: Asymptotic Analysis, vol. 32, no. 3-4, pp. 359-359, 2002