Integral approach to sensitive singular perturbations

Nicolas Meunier; Evariste Sanchez-Palencia

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arXiv · 0910.2087

Integral approach to sensitive singular perturbations

Nicolas Meunier·Evariste Sanchez-Palencia

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Abstract

We consider singular perturbation elliptic problems depending on a parameter ? such that, for ? = 0 the boundary conditions are not adapted to the equation (they do not satisfy the Shapiro - Lopatinskii condition). The limit only holds in very abstract spaces out of distribution theory involving complexi?cation and non-local phenomena. We give a very elementary model problem showing the main features of the limit process, as well as a heuristic integral procedure for obtain- ing a description of the solutions for small ?. Such kind of problems appear in thin shell theory when the middle surface is elliptic and the shell is fixed by a part of the boundary and free by the rest.

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Nicolas Meunier, Evariste Sanchez-Palencia. 2009-10-12. Integral approach to sensitive singular perturbations. https://arxiv.org/abs/0910.2087

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