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Weakly semibounded boundary problems and sesquilinear forms

Gerd Grubb (1973)

Annales de l'institut Fourier

Let A be a 2 m order differential operator in a hermitian vector bundle E over a compact riemannian manifold Ω with boundary Γ  ; and denote by A B the realization defined by a normal differential boundary condition B ρ u = 0 ( u H 2 m ( E ) , ρ u = Cauchy data). We characterize, by an explicit condition on A and B near Γ , the realizations A B for which there exists an integro-differential sesquilinear form a B ( u , ν ) on H m ( E ) such that ( A u , ν ) = a B ( u , ν ) on D ( A B ) ; moreover we show that these are exactly the realizations satisfying a weak semiboundedness estimate:...

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