Restricted accessResearch articleFirst published online 2020-3-27
A uniformly valid model for the limiting behaviour of voltage potentials in the presence of thin inhomogeneities II. A local energy approximation result
In this second part of a two part paper, we establish a local, uniform
energy-approximation estimate for the solutions to a simplified model of thin
inhomogeneities with open mid-curves. This local result plays a crucial role in the proof
of the global, uniform approximation results established in the first part of this paper
(Asymptotic Analysis (2019)).
For more details about the model we also refer the reader to (Chinese Annals of
Mathematics, Series B38 (2017) 293–344).
M.Charnley and
M.S.Vogelius, A
uniformly valid model for the limiting behaviour of voltage potentials in the presence of
thin inhomogeneities I. The case of an open mid-curve, Asymptotic
Analysis (2019).
2.
C.Dapogny and
M.S.Vogelius,
Uniform asymptotic expansion of the voltage potential in the presence of
thin inhomogeneities with arbitrary conductivity, Chinese Annals
of Mathematics, Series B38 (2017), 293–344.
doi:10.1007/s11401-016-1072-3.
3.
J.-L.Lions and
E.Magenes,
Non-Homogeneous Boundary Value Problems and Applications I,
Grundlehren der Mathematischen Wissenschaften,
Vol. 181, Springer-Verlag,
Berlin/Heidelberg/New York,
1972.
4.
D.Morgenstern and
I.Szabo,
Vorlesungen über Theoretische Mechanik, Die Grundlehren der
Mathematischen Wissenschaften in Einzeldarstellungen,
Vol. 112, Springer-Verlag,
Berlin–Göttingen–Heidelberg,
1961.
