Castro, L. P., Pesetskaya, E., Rogosin, S. V. (2009). Effective conductivity of a composite material with non-ideal contact conditions. Complex variables and elliptic equations, 54 (12), 1085-1100.The effective conductivity of 2D doubly periodic composite materials with circular disjoint inclusions under non-ideal contact conditions on the boundary between material components is found. The obtained explicit formula for the effective conductivity contains all parameters of the considered model, such as the conductivities of matrix and inclusions, resistance coefficients, radii and centres of the inclusions and also the values of special Eisenstein functions. The method of functional equations is used to analyse the conjugation problem for analytic functions which is equivalently derived from the initial problem. Existence and uniqueness for the solution of the problem is obtained by using a reduction to a certain mixed boundary value problem for analytic functions in special functional spaces.Peer reviewe

No abstract

The main objective is the study of a class of boundary value problems in weak formulation where two boundary conditions are given on the halflines bordering the first quadrant that contain impedance data and oblique derivatives. The associated operators are reduced by matricial coupling relations to certain boundary pseudodifferential operators which can be analyzed in detail. Results are: Fredholm criteria, explicit construction of generalized inverses in Bessel potential spaces, eventually after normalization, and regularity results. Particular interest is devoted to the impedance problem and to the oblique derivative problem, as well. Mathematics Subject Classification (2000). Primary 35J25; Secondary 30E25, 47G30, 45E10, 47A53, 47A20.

No abstract

Dedicated to the memory of Erhard Meister with gratitude and admirationWe consider convolution type operators that carry a certain symmetry in their structure. The study is motivated by several applications in mathematical physics where this kind of operators appears. They can be regarded as a class of Wiener-Hopf plus Hankel operators acting in spaces of Bessel potentials. But the common approach of reduction to systems of Wiener-Hopf equations is avoided by a more direct factorization scheme. The main results are: Fredholm criteria, analytical representation of generalized inverses, and the constructive solution of normalization problems.