Almut Veraat (Imperial College London)
Magnus Goffeng (Lund University)
Using a Bär-Ballmann type machinery, one can describe all realizations of elliptic operators on manifolds with boundary. Classically, boundary value problems are phrased in terms of imposing a boundary condition on a functions values and derivatives on the boundary. A natural line of questioning is to ask to what extent classical results for boundary value problems extend to general boundary conditions? In this talk, we show that the Weyl law extend to all self-adjoint regular realizations of a formally self-adjoint elliptic differential operator with positive principal symbol. This produces an explicit asymptotical formula for the eigenvalues. As is the case for classical boundary conditions or on compact manifolds, the leading term only sees the principal symbol. Based on joint work with Lashi Bandara and Hemanth Saratchandran.
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