| Grant number: | 18/02663-0 |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |
| Start date: | September 01, 2018 |
| End date: | October 31, 2018 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Analysis |
| Principal Investigator: | Gustavo Hoepfner |
| Grantee: | Gustavo Hoepfner |
| Visiting researcher: | Andrew Seth Raich |
| Visiting researcher institution: | University of Arkansas, United States |
| Host Institution: | Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil |
Abstract
We want to study regularity of partial differential equations inthe space of global $L^q$ Gevrey functions, recently introduced in [Z. Adwan, G. Hoepfner, and A. Raich, Global Lq-Gevrey functions and their applications, J. Geom. Anal. 27 (2017), no. 3, 1874-1913.] and [G. Hoepfner and A. Raich, Global Lq Gevrey functions, Paley-Weiner theorems, and the FBI transform, to appear, Indiana Univ. Math. J.] and in a generalized and new function space called the space of global $L^q$ Denjoy-Carleman functions.We aim to develop a wedge approach similar to a celebrated Bony's theorem [J. M. Bony, Équivalence des diverses notions de spectre singulier analytique, Séminaire Goulaouic-Schwartz (1976/1977), E quations aux dérivées partielles et analysefonctionnelle, Exp.No.3, CentreMath., École Polytech., Palaiseau,1977.] and among other results, we will focus on three main topics. The first establishes the existence of boundary values of continuous functions on a wedge. Next, we borrow the FBI transform approach from [G. Hoepfner and A. Raich, Global Lq Gevrey functions, Paley-Weiner theorems, and the FBI transform, to appear, Indiana Univ. Math. J.] to define global wavefront sets and try to prove a relationship between the inclusion of a direction in the global wavefront set and the existence of boundary values of sums of weighted $L^p$ functions defined in wedges. The last is an classical application namely, the relationship between the global characteristic set of a partial differential operator $P$ and the microglobal wavefront sets of $u$ and $Pu$. We also want to investigate other relations with this $L^q$ Global Denjoy-Carleman functions such as: Hardy spaces properties and the Grusin operator. (AU)
| Articles published in Agência FAPESP Newsletter about the research grant: |
| More itemsLess items |
| TITULO |
| Articles published in other media outlets ( ): |
| More itemsLess items |
| VEICULO: TITULO (DATA) |
| VEICULO: TITULO (DATA) |