Uniform Asymptotic Expansion of the Voltage Potential in the Presence of Thin Inhomogeneities with Arbitrary Conductivity

Contents 1. Introduction 1 2. Preliminaries and main notations 2 2.1. Setting of the problem 2 2.2. Some facts about distances and projections 4 3. A general argument to estimate the difference between energy minimizers 5 3.1. An energy lemma 6 3.2. Extension of Lemma 3 to the case of inhomogeneous Dirichlet boundary conditions 7 4. Derivation of the 0 th order approximation of u ε 9 4.1. Asymptotic expansions of the energy functionals associated with u ε 9 5. Study of the approximate function u 0 ε : uniform energy and regularity estimates 14 5.1. Existence, uniqueness, and a classical formulation of (4.10) 14 5.2. The dual energy maximization problem for u