engleski

Friedrichs operators as dual pairs

The Friedrichs (1958) theory of positive symmetric systems of first order partial differential equations encompasses many standard equations of mathematical physics, irrespective of their type. This theory was recast in an abstract Hilbert space setting by Ern, Guermond and Caplain (2007), and by Antonić and Burazin (2010). In this work we make a further step, presenting a purely operator-theoretic description of abstract Friedrichs systems via the universal operator extension theory of dual pairs (Grubb, 1968). For a given Friedrichs system the existence of a boundary condition such that the problem is well-posed is shown, as well as a classification of all such boundary conditions.

Symmetric positive first-order system of partial differential equations ; Krein space ; Universal parametrisation of extensions

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