Geodesic
Construction of a natural norm for the convection-diffusion-reaction operator
Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 2, pp. 335-355.

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In this work, we construct, by means of the function space interpolation theory, a natural norm for a generic linear coercive and non-symmetric operator. We look for a norm which is the counterpart of the energy norm for symmetric operators. The natural norm allows for continuity and inf-sup conditions independent of the operator. Particularly we consider the convection-diffusion-reaction operator, for which we obtain continuity and inf-sup conditions that are uniform with respect to the operator coefficients, and therefore meaningful in the convectiondominant regime. Our results are preliminary to a deeper understanding and analysis of the numerical techniques for non-symmetric problems.
In questo lavoro si costruisce, mediante interpolazione, una norma naturale per operatori lineari continui coercivi e non simmetrici. Più precisamente, si cerca una norma con stesse le proprietà che ha la norma dell'energia quando si considerano operatori simmetrici: si dimostrano cioè, rispetto a tale norma, stime di continuità e di inf-sup indipendenti dall'operatore. In particolare, si prende in considerazione l'operatore di diffusione-trasporto-reazione lineare: si ottengono quindi stime di continuità e inf-sup indipendenti dai coefficienti dell'operatore, pertanto significative anche nel regime di trasporto dominante. I risultati qui presentati possono servire ad una più approfindita comprensione e analisi di tecniche numeriche per problemi non simmetrici. 
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Sangalli, Giancarlo. Construction of a natural norm for the convection-diffusion-reaction operator. Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 2, pp. 335-355. http://geodesic.mathdoc.fr/item/BUMI_2004_8_7B_2_a4/

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