A Spectral Sobolev Problem for the Biharmonic Operator

Abstract Consider the biharmonic operator on the 3-dimensional torus with the domain given by functions vanishing on a circle inside the torus. We describe explicitly the adjoint operator and the Friedrichs extension. More precisely, we show that the Friedrichs extension is a Sobolev problem with boundary and coboundary conditions along the circle. Bibliography: 27 items.

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