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Matrix triangulation of hypoelliptic boundary value problems

R. A. Artino, J. Barros-Neto (1992)

Annales de l'institut Fourier

Given a hypoelliptic boundary value problem on ω × [ 0 , T ) with ω an open set in 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.

Multivariate Sturm-Habicht sequences: real root counting on n-rectangles and triangles.

Laureano González-Vega, Guadalupe Trujillo (1997)

Revista Matemática de la Universidad Complutense de Madrid

The main purpose of this note is to show how Sturm-Habicht Sequence can be generalized to the multivariate case and used to compute the number of real solutions of a polynomial system of equations with a finite number of complex solutions. Using the same techniques, some formulae counting the number of real solutions of such polynomial systems of equations inside n-dimensional rectangles or triangles in the plane are presented.

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