Matrix triangulation of hypoelliptic boundary value problems

Artino, R. A.; Barros-Neto, J.

Annales de l'Institut Fourier, Tome 42 (1992) no. 4, pp. 805-824.

Étant donné un problème aux limites dans $\Omega \times [0,T]$ avec $\Omega$ ouvert de ${\mathbf{R}}^n$, $(n>1)$, nous réduisons, par le procédé de triangulation des matrices, le problème donné à deux systèmes du premier ordre, et étudions des majorations des valeurs propres des matrices correspondantes. L’hypoellipticité jusqu’à la frontière est donc caractérisée en termes de l’opérateur de Calderon associé au problème donné.

Given a hypoelliptic boundary value problem on $\omega \times [0,T)$ with $\omega$ an open set in ${\mathbf{R}}^n$, $(n>1)$, we show by matrix triangulation how to reduce it to two uncoupled first order systems, and how to estimate the eigenvalues of the corresponding matrices. Parametrices for the first order systems are constructed. We then characterize hypoellipticity up to the boundary in terms of the Calderon operator corresponding to the boundary value problem.

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