Otar Chkadua and David Natroshvili
abstract:
The paper deals with the three-dimensional Robin type boundary value problem (BVP)
of piezoelasticity for anisotropic inhomogeneous solids and develops the
generalized potential method based on the use of localized parametrix. Using
Green's integral representation formula and properties of the localized layer
and volume potentials, we reduce the Robin type BVP to the localized
boundary-domain integral equations (LBDIE) system. First we establish the
equivalence between the original boundary value problem and the corresponding
LBDIE system. We establish that the obtained localized boundary-domain integral
operator belongs to the Boutet de Monvel algebra and by means of the
Vishik-Eskin theory based on the Wiener-Hopf factorization method, we derive
explicit conditions under which the localized operator possesses Fredholm
properties and prove its invertibility in appropriate Sobolev-Slobodetskii and
Bessel potential spaces.
Mathematics Subject Classification: 35J25, 31B10, 45K05, 45A05
Key words and phrases: Piezoelasticity, partial differential equations with variable coefficients, boundary value problems, localized parametrix, localized boundary-domain integral equations, pseudo-differential operators