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Asymptotics of potentials in the edge calculus

D. KapanadzeB.-W Schulze — 2006

Bollettino dell'Unione Matematica Italiana

Boundary value problems on manifolds with conical singularities or edges contain potential operators as well as trace and Green operators which play a similar role as the corresponding operators in (pseudo-differential) boundary value problems on a smooth manifold. There is then a specific asymptotic behaviour of these operators close to the singularities. We characterise potential operators in terms of actions of cone or edge pseudo-differential operators (in the neighbouring space) on densities...

Pseudo-Differential Operators in a Wave Diffraction Problem with Impedance Conditions

Castro, L.P.Kapanadze, D. — 2008

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 35J05, 35J25, 35C15, 47H50, 47G30 We consider an impedance boundary-value problem for the Helmholtz equation which models a wave diffraction problem with imperfect conductivity on a strip. Pseudo-differential operators are used to deal with this wave diffraction problem. Therefore, single and double layer potentials allow a reformulation of the problem into a system of integral equations. By using operator theoretical methods, the well-posedness...

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