Some topics on the regularity of analytic-Gevrey vectors
My aim is to give, in this talk, some topics on the question of regularity of Analytic-Gevrey vectors of partial differential operators (p.d.o.) with analytic-Gevrey coefficients. Since the results obtained in the sixties on elliptic p.d.o's, which are both hypoelliptic (C∞ setting), analytic-G...
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| Format: | Article |
| Language: | English |
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University of Bologna
2024-01-01
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| Series: | Bruno Pini Mathematical Analysis Seminar |
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| Online Access: | https://mathematicalanalysis.unibo.it/article/view/18858 |
| _version_ | 1797359630277410816 |
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| author | Makhlouf Derridj |
| author_facet | Makhlouf Derridj |
| author_sort | Makhlouf Derridj |
| collection | DOAJ |
| description | My aim is to give, in this talk, some topics on the question of regularity of Analytic-Gevrey vectors of partial differential operators (p.d.o.) with analytic-Gevrey coefficients. Since the results obtained in the sixties on elliptic p.d.o's, which are both hypoelliptic (C∞ setting), analytic-Gevrey hypoelliptic (analytic-Gevrey setting) and satisfy the so-called Kotake-Narasimhan property, a lot of works and articles were devoted to these problems in case of non elliptic p.d.o's under suitable hypotheses (for example on the degeneracy of ellipticity). I will consider the third problem on analytic-Gevrey vectors in the three cases of global (on compact manifolds), local (near a point in the base-space), microlocal (near a point in the cotangent space), situations, and say few words on the main two methods used in order to obtain positive (or negative) results. Finally I will focus on some new microlocal results on degenerate elliptic (also called sub-elliptic) p.d.o's of second order, obtained in a common work with Gregorio Chinni. |
| first_indexed | 2024-03-08T15:26:31Z |
| format | Article |
| id | doaj.art-753dda3331ca46b78594c580c666e47f |
| institution | Directory Open Access Journal |
| issn | 2240-2829 |
| language | English |
| last_indexed | 2024-03-08T15:26:31Z |
| publishDate | 2024-01-01 |
| publisher | University of Bologna |
| record_format | Article |
| series | Bruno Pini Mathematical Analysis Seminar |
| spelling | doaj.art-753dda3331ca46b78594c580c666e47f2024-01-10T08:48:10ZengUniversity of BolognaBruno Pini Mathematical Analysis Seminar2240-28292024-01-011427710010.6092/issn.2240-2829/1885817220Some topics on the regularity of analytic-Gevrey vectorsMakhlouf Derridj05, Rue de la Juviniére, 78350 Les Loges en Josas, FranceMy aim is to give, in this talk, some topics on the question of regularity of Analytic-Gevrey vectors of partial differential operators (p.d.o.) with analytic-Gevrey coefficients. Since the results obtained in the sixties on elliptic p.d.o's, which are both hypoelliptic (C∞ setting), analytic-Gevrey hypoelliptic (analytic-Gevrey setting) and satisfy the so-called Kotake-Narasimhan property, a lot of works and articles were devoted to these problems in case of non elliptic p.d.o's under suitable hypotheses (for example on the degeneracy of ellipticity). I will consider the third problem on analytic-Gevrey vectors in the three cases of global (on compact manifolds), local (near a point in the base-space), microlocal (near a point in the cotangent space), situations, and say few words on the main two methods used in order to obtain positive (or negative) results. Finally I will focus on some new microlocal results on degenerate elliptic (also called sub-elliptic) p.d.o's of second order, obtained in a common work with Gregorio Chinni.https://mathematicalanalysis.unibo.it/article/view/18858microlocal regularitygevrey vectorsdegenerate elliptic-parabolic differential operators |
| spellingShingle | Makhlouf Derridj Some topics on the regularity of analytic-Gevrey vectors Bruno Pini Mathematical Analysis Seminar microlocal regularity gevrey vectors degenerate elliptic-parabolic differential operators |
| title | Some topics on the regularity of analytic-Gevrey vectors |
| title_full | Some topics on the regularity of analytic-Gevrey vectors |
| title_fullStr | Some topics on the regularity of analytic-Gevrey vectors |
| title_full_unstemmed | Some topics on the regularity of analytic-Gevrey vectors |
| title_short | Some topics on the regularity of analytic-Gevrey vectors |
| title_sort | some topics on the regularity of analytic gevrey vectors |
| topic | microlocal regularity gevrey vectors degenerate elliptic-parabolic differential operators |
| url | https://mathematicalanalysis.unibo.it/article/view/18858 |
| work_keys_str_mv | AT makhloufderridj sometopicsontheregularityofanalyticgevreyvectors |