Analysis of united boundary-domain integro-differential and integral equations for a mixed BVP with variable coefficient

✍ Scribed by Sergey E. Mikhailov

• Publisher: John Wiley and Sons
• Year: 2006
• Tongue: English
• Weight: 209 KB
• Volume: 29
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.706

✦ Synopsis

The mixed (Dirichlet-Neumann) boundary-value problem for the 'Laplace' linear di erential equation with variable coe cient is reduced to boundary-domain integro-di erential or integral equations (BDIDEs or BDIEs) based on a specially constructed parametrix. The BDIDEs=BDIEs contain integral operators deÿned on the domain under consideration as well as potential-type operators deÿned 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-di erential 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.