𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Uniform convergence of a singular perturbation problem

✍ Scribed by Luis A. Caffarelli; Antonio Córdoba

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
355 KB
Volume
48
Category
Article
ISSN
0010-3640

No coin nor oath required. For personal study only.

✦ Synopsis

where the interface bRl n R = bR2 n R is a "regular" surface with minimal area. This problem has been analyzed, among others, by De Giorgi, Franzone, and Ambrogio in [3] and[4], Can, Gurtin, and Slemrod in [2], Alikakos and Shaing in [l], Modica in [7], Modica and Mortola in [8], Kohn and Sternberg in [6], and Frohlich and Struwe in [5]. Let us mention especially the work of L. Modica in [7] where the following theorem is proved THEOREM. Fix M E R! such that u' IRI < M < u21RI and suppose that the function u, is, for every E > 0, a solution of the variational problem If { E h } is a sequence of positive numbers such that Eh 1 0 and U,h converges in L'(R) to afunction uo, then we have: (i) ~( u o ( x ) ) = O (i.e., uo(x) = u' or u&) = u2) a.e. x E R.

📜 SIMILAR VOLUMES

Uniform convergence of discretization er
Uniform convergence of discretization error for a singular perturbation problem
✍ P. Wesseling 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 544 KB

Cell-centered discretization of the convection-diffusion equation with large PCclet number Pe is analyzed, in the presence of a parabolic boundary layer. It is shown theoretically how, by suitable mesh refinement in the boundary layer, the accuracy can be made to be uniform in Pe, at the cost of a I

Critical Points of a Singular Perturbati
Critical Points of a Singular Perturbation Problem via Reduced Energy and Local Linking
✍ Nicholas Alikakos; Michał Kowalczyk 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 208 KB

In this paper we study the existence of critical points of the functional where 0 # R d , d 2 is a bounded domain with C 3 boundary, u # H 1 (0), and = is a small parameter. On the nonlinearity F we assume: ). Additionally we require that there exists q>1 such that for u>0 the function F$(u)Âu q i