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Abstract

We consider boundary value problems of anti-plane shear in the static theory of linear piezoelectricity. Using the boundary integral equation method, we reduce the problems to systems of singular integral equations to which Nöether's classical theorems on existence of solution are shown to apply. Moreover, it is shown that for the boundary value problems considered here, Nöether's theorems actually reduce to Fredholm's theorems. This allows us to establish well-posedness results and find integral potential-type solutions of the corresponding boundary value problems for a rather general class of piezoelectric materials.

Keywords

linear piezoelectricity anti-plane elasticity integral equatios existence and uniqueness

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References

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Integral Solutions of Boundary Value Problems of Anti-Plane Piezoelectricity

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