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Research Article
Analysis of united boundary-domain integro-differential and integral equations for a mixed BVP with variable coefficient
Article first published online: 20 DEC 2005
DOI: 10.1002/mma.706
Copyright © 2005 John Wiley & Sons, Ltd.
1099-1476/asset/cover.gif?v=1&s=7f3c8599d848bbeeab682f114551621db8fd932e "Mathematical Methods in the Applied Sciences")
Additional Information
How to Cite
Mikhailov, S. E. (2006), Analysis of united boundary-domain integro-differential and integral equations for a mixed BVP with variable coefficient. Math. Meth. Appl. Sci., 29: 715–739. doi: 10.1002/mma.706
Publication History
- Issue published online: 22 FEB 2006
- Article first published online: 20 DEC 2005
- Manuscript Accepted: 30 OCT 2005
- Manuscript Revised: 26 OCT 2005
- Manuscript Received: 8 OCT 2004
- Abstract
- References
- Cited By
Keywords:
- integral equations;
- integro-differential equations;
- parametrix;
- partial differential equations;
- variable coefficients;
- mixed boundary-value problem;
- Sobolev spaces;
- equivalence;
- invertibility
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. Copyright © 2005 John Wiley & Sons, Ltd.