The functional dissipativity of certain systems of partial differential equations

2022/08/15 by Cialdea, Alberto, Maz'ya, Vladimir
#35J47 #47B44 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2208.07456

Abstract

In the present paper we consider the functional dissipativity of the Dirichlet problem for systems of partial differential operators of the form ∂_h (\mathop\mathscr A\nolimits^hk(x)∂_k) (\mathop\mathscr A\nolimits^hk being m× m matrices with complex valued L¹_loc entries). In the particular case of the operator ∂_h (\mathop\mathscr A\nolimits^h(x)∂_h) (where \mathop\mathscr A\nolimits^h are m× m matrices) we obtain algebraic necessary and sufficient conditions. We give also three different notions of functional ellipticity and investigate the relations between them and the functional dissipativity for the operators in question.

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