Naslov
Classification of classical Friedrichs differential operators: One-dimensional scalar case

Autori
Erceg, Marko ; Soni, Sandeep Kumar

Izvornik
Communications on pure and applied analysis (1534-0392) 21 (2022), 10; 3499-3527

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
symmetric positive first-order system of partial differential equations ; dual pairs ; indefinite inner product space ; universal parametrisation of extensions

Sažetak
The theory of abstract Friedrichs operators, introduced by Ern, Guermond and Caplain (2007), proved to be a successful setting for studying positive symmetric systems of first order partial differential equations (Friedrichs, 1958), nowadays better known as Friedrichs systems. Recently, Antonić, Michelangeli and Erceg (2017) presented a purely operator-theoretic description of abstract Friedrichs operators, allowing for application of the universal operator extension theory (Grubb, 1968). In this paper we make a further theoretical step by developing a decomposition of the graph space (maximal domain) as a direct sum of the minimal domain and the kernels of corresponding adjoints. We then study one-dimensional scalar (classical) Friedrichs operators with variable coefficients and present a complete classification of admissible boundary conditions.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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