Abstract
The solution of systems of finite-part singular integral equations defined in L p with many applications in mathematical physics is investigated. A finite-part singular integral representation analysis in L p is proposed, by proving that every system of finite-part singular integral equations is equivalent to an additional system of Fredholm equations. Some finite-part singular integral equation solubility theorems defined in L p are further presented, by applying the index of the finite-part singular integral equations. A fracture mechanics application is finally given, for the determination of the stress intensity factors at the tips of a crack normal to a bimaterial interface.
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