Asymptotic Analysis - Volume 8, issue 1

Authors: Cioranescu, Doina | Oleinik, O. A. | Tronel, Gerard

Article Type: Research Article

Abstract: In paper [1] Korn's inequalities are obtained for frame type structures and junctions. For such kind of domains, depending on several parameters, the constants in Korn's inequalities are given in a form which points out their dependence on these parameters and on the geometry of the domain. We improve here these estimates, we give the full proofs of them and show that the constants we obtain are asymptotically sharp. We also correct some misprints from paper [1].

DOI: 10.3233/ASY-1994-8101

Citation: Asymptotic Analysis, vol. 8, no. 1, pp. 1-14, 1994

Authors: Böttcher, Albrecht | Wolf, Hartmut

Article Type: Research Article

Abstract: We establish a criterion for the asymptotic invertibility of Toeplitz operators with continuous symbols on weighted Bergman spaces of the polydisk and their formal limit, the multi-dimensional Bargmann space.

DOI: 10.3233/ASY-1994-8102

Citation: Asymptotic Analysis, vol. 8, no. 1, pp. 15-33, 1994

Authors: Widom, Harold

Article Type: Research Article

Abstract: We consider the problem of the asymptotics of tr f(Tα ) where f is a “general” function, Tα , the pseudodifferential operator with symbol σ(x,ξ,α). Here α is a large parameter, and σ is a rapidly decreasing function. If σ smooth, techniques which are by now standard yield complete asymptotic expansions, with computable coefficients, as α→∞. Here we consider also cases where σ is not smooth; it may jump across a hypersurface in x-space or a hyperplane in x, ξ-space. We prove the existence of complete asymptotic expansions and show how to compute the coefficients for polynomial f. Of central …importance is the analytic continuations of certain distributions acting on spaces of non-smooth test functions. Show more

DOI: 10.3233/ASY-1994-8103

Citation: Asymptotic Analysis, vol. 8, no. 1, pp. 35-63, 1994

Authors: Siedentop, Heinz | Weikard, Rudi

Article Type: Research Article

Abstract: We prove that the semi-classical expression for the sum of the negative eigenvalues of a one-dimensional Schrödinger operator with negative potential −φ is correct up to order O(h log 1/h) in the “Planck” constant h provided φ1/4 is in the Sobolev space H1 (R).

DOI: 10.3233/ASY-1994-8104

Citation: Asymptotic Analysis, vol. 8, no. 1, pp. 65-72, 1994

Authors: da Silva Ferreira, José

Article Type: Research Article

Abstract: We study the exponential decay of the energy of the nonlinear system of Klein–Gordon equations utt −Δu+m1 u+f(u,v)+a(x)ut =0, vtt −Δv+m2 v+g(u,v)+b(x)vt =0,(x,t)∈O×(0,∞),u=v=0 on Γ0 ×(0,∞), where O is abounded or unbounded domain in RN with smooth boundary ro Γ0 :=∂O;a,b∈L∞ + O,a,b≥constant>0, a.e. in some appropriated open subset of O, and f, g satisfy some suitable conditions. The exponential decay of the energy is established by adapting to the system multiplier techniques of J.L. Lions, some techniques developed by E. Zuazua for a single equation and a unique continuation principle of A. Ruiz.

DOI: 10.3233/ASY-1994-8105

Citation: Asymptotic Analysis, vol. 8, no. 1, pp. 73-92, 1994

Authors: Cantarelli, Giancarlo

Article Type: Research Article

Abstract: The methods introduced in [3–5], that is comparison method together with the use of suitable Liapunov functions, are generalized and applied to the study of global existence of solutions of ‘generalized’ Lagrange equations. New criteria are obtained which extend various results of [6] and [7].

DOI: 10.3233/ASY-1994-8106

Citation: Asymptotic Analysis, vol. 8, no. 1, pp. 93-101, 1994

Article Type: Correction

DOI: 10.3233/ASY-1994-8107

Citation: Asymptotic Analysis, vol. 8, no. 1, pp. 103-103, 1994