Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
Georges Habib (Lebanese University, Beirut)
In this talk, we shall introduce the notion of biharmonic Steklov operator, which we then extend to differential forms. The definition is motivated by the extension of the Serrin problem to differential forms. We study the spectral properties of this operator and show that it has a discrete spectrum consisting of eigenvalues with finite multiplicities. We then estimate its lowest eigenvalue in terms of geometric quantities and relate it to other boundary problems, Dirichlet, Neumann and Robin.
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