Asymptotic Analysis - Volume 1, issue 3

Authors: Esteban, M.J. | Lions, P.L.

Article Type: Research Article

Abstract: It was already known that when the topological charge k is larger than 1, the ground state energy for Skyrme's problem can never be achieved by a hedge-hog type function. In this paper we prove that in fact the ratio of the ground state energy to the lower bound of the energy for the hedge-hog functions converges to 0 as k−1 .

DOI: 10.3233/ASY-1988-1301

Citation: Asymptotic Analysis, vol. 1, no. 3, pp. 187-192, 1988

Authors: Brüning, Jochen | Schröder, Herbert

Article Type: Research Article

Abstract: The classical result of Minakshisundaram and Pleijel on the asymptotic expansion of the trace of the heat semigroup associated with the Laplacean on a compact Riemannian manifold M has been generalized by Brüning and Heintze to the case that a compact group is acting on M by isometries. They obtained an asymptotic expansion involving logarithmic terms. Here we prove that these terms vanish if M has constant sectional curvature or if M is a warped product M=[0,π]×f Sn with n≥2 and suitable f.

DOI: 10.3233/ASY-1988-1302

Citation: Asymptotic Analysis, vol. 1, no. 3, pp. 193-203, 1988

Authors: Tatsien, Li | Qi, Tang

Article Type: Research Article

Abstract: In this paper we present and discuss a class of problems of boundary homogenization for parabolic equations, and point out its application to the heat analysis of a car wheel.

DOI: 10.3233/ASY-1988-1303

Citation: Asymptotic Analysis, vol. 1, no. 3, pp. 205-212, 1988

Authors: Penzel, F.

Article Type: Research Article

Abstract: The asymptotical behaviour of the solution of (n×n)-systems of singular integral equations with piecewise Hoelder-continuous coefficients is described, even if the explicit solution is not known.

DOI: 10.3233/ASY-1988-1304

Citation: Asymptotic Analysis, vol. 1, no. 3, pp. 213-225, 1988

Authors: Charbonnel, Anne-Marie

Article Type: Research Article

Abstract: We consider ν pseudodifferential operators, Q1 (h),…,Qν (h), acting in Rn , commuting together, depending on a small parameter h. For instance, one of them is the Schrödinger operator with a potential V(x) satisfying the condition $\underline{lim}_{|x|\rightarrow +\infty}V(x)>E$ . Under suitable conditions, we establish a functional ca1culus to define f(Q1 (h),…,Qν (h)) as a pseudodifferential operator of the same type, when f belongs to C∞ 0 (Rν ). We use it to study the semiclassical behaviour of the joint spectrum of Q1 (h),…,Qν (h), lying in a compact of Rν where it is discrete. When these operators form …a quantically integrable system, we give more precise estimations. Our results generalize those obtained by Helffer and Robert for one operator acting in Rn . Show more

DOI: 10.3233/ASY-1988-1305

Citation: Asymptotic Analysis, vol. 1, no. 3, pp. 227-261, 1988