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|Title:||Analysis of united boundary-domain integro-differential and integral equations for a mixed BVP with variable coefficient|
|Keywords:||Integral equations; Integro-differential equations; Parametrix; Partial differential equations; Variable coefficients; Mixed boundary-value problem; Sobolev spaces; Equivalence; Invertibility|
|Citation:||Mathematical Methods in the Applied Sciences. 29 (6): 715-739|
|Abstract:||The mixed (Dirichlet-Neumann) boundary-value problem for the Laplace linear differential equation with variable coefficient is reduced to boundary-domain integro-differential or integral equations (BDIDEs or BDIEs) based on a specially constructed parametrix. The BDIDEs/BDIEs contain integral operators defined on the domain under consideration as well as potential-type operators defined on open sub-manifolds of the boundary and acting on the trace and/or co-normal derivative of the unknown solution or on an auxiliary function. Some of the considered BDIDEs are to be supplemented by the original boundary conditions, thus constituting boundary-domain integro-differential problems (BDIDPs). Solvability, solution uniqueness, and equivalence of the BDIEs/BDIDEs/BDIDPs to the original BVP, as well as invertibility of the associated operators are investigated in appropriate Sobolev spaces.|
|Appears in Collections:||Mathematical Science|
Dept of Mathematics Research Papers
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