Given a hypoelliptic boundary value problem on with an open set in , , 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.
Étant donné un problème aux limites dans avec ouvert de , , 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.
@article{AIF_1992__42_4_805_0, author = {Artino, R. A. and Barros-Neto, J.}, title = {Matrix triangulation of hypoelliptic boundary value problems}, journal = {Annales de l'Institut Fourier}, pages = {805--824}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {42}, number = {4}, year = {1992}, doi = {10.5802/aif.1310}, zbl = {0758.35098}, mrnumber = {93k:35287}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1310/} }
TY - JOUR AU - Artino, R. A. AU - Barros-Neto, J. TI - Matrix triangulation of hypoelliptic boundary value problems JO - Annales de l'Institut Fourier PY - 1992 SP - 805 EP - 824 VL - 42 IS - 4 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1310/ DO - 10.5802/aif.1310 LA - en ID - AIF_1992__42_4_805_0 ER -
%0 Journal Article %A Artino, R. A. %A Barros-Neto, J. %T Matrix triangulation of hypoelliptic boundary value problems %J Annales de l'Institut Fourier %D 1992 %P 805-824 %V 42 %N 4 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.1310/ %R 10.5802/aif.1310 %G en %F AIF_1992__42_4_805_0
Artino, R. A.; Barros-Neto, J. Matrix triangulation of hypoelliptic boundary value problems. Annales de l'Institut Fourier, Volume 42 (1992) no. 4, pp. 805-824. doi : 10.5802/aif.1310. https://aif.centre-mersenne.org/articles/10.5802/aif.1310/
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