Reciprocity gap method for inclusions with variable conductivity
Year: 2026
Type: article
Abstract: We extend the reciprocity gap approximation theorem proved by Di Cristo and Milan (2020) to the case of spatially varying conductivity coefficients. We consider conductivities of the form γ ( x ) = a ( x ) + b ( x ) χ D ( x ) where a , b ∈ L ∞ ( Ω ) satisfy uniform ellipticity conditions. We show that the fundamental dichotomy underlying the reciprocity gap method, based on bounded approximating sequences for sampling points inside the inclusion and blow-up outside, remains valid without assuming piecewise constant conductivity. The proof relies on variational arguments and weighted transmission conditions and does not require additional regularity of the inclusion.
Source: Applied Mathematics Letters
Author: Michele Di Cristo
Institution: Politecnico di Milano
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,800
OpenAlex ID: W7153999645