Summary
Consider the Dirichlet problem for an elliptic equation in a domain Ω, with coefficients having discontinuity on a surface Γ. Suppose Γ divides Ω into Ω1∪ Ω2(Ω2 the inner core), the thickness of Ω1 is of order of magnitude ɛ, and the modulus of ellipticity in Ω1 is of order magnitude λ1. The asymptotic behavior of the solution is studied as ɛ → 0, λ1 → 0, provided lim (ɛ/λ1) exists. Other questions of this type are studied both for elliptic equations and for elliptic variational inequalities.
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The second author is partially supported by National Science Foundation Grant 7406375 A01. The third author is partially supported by National Science Foundation Grant MC575-21416 A01.
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Brezis, H., Caffarelli, L.A. & Friedman, A. Reinforcement problems for elliptic equations and variational inequalities. Annali di Matematica pura ed applicata 123, 219–246 (1980). https://doi.org/10.1007/BF01796546
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DOI: https://doi.org/10.1007/BF01796546