Global ultradifferentiable functions, complex analysis, and PDE's
Regularity theory for classes of local and non-local degenerate elliptic equation
Development of a novel microbial biofertilizer with activity against effects of w...
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| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP - Brazil
[2] 1 Univ Arkansas, Dept Math Sci, SCEN 309, Fayetteville, AR 72701 - USA
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | MATHEMATISCHE ZEITSCHRIFT; v. 291, n. 3-4, p. 971-998, APR 2019. |
| Web of Science Citations: | 1 |
| Abstract | |
In this paper, we begin the study of regularity of partial differential equations in the space of global Lq Gevrey functions, recently introduced in Adwan et al. (J Geom Anal 27(3):1874-1913, 2017) and Hoepfner and Raich (Indiana Univ Math J, forthcoming) and in a generalized and new function space called the space of global Lq Denjoy-Carleman functions. We develop a wedge approach similar to Bony's theorem (Bony in Seminaire Goulaouic-Schwartz (1976/1977), Equations aux derivees partielles et analyse fonctionnelle, Exp No 3. Centre Math, Ecole Polytech, Palaiseau, 1977) and prove three main theorems. The first establishes the existence of boundary values of continuous functions on a wedge. Next, we borrow the FBI transform approach from Hoepfner and Raich (forthcoming) to define global wavefront sets and prove a relationship between the inclusion of a direction in the global wavefront set and the existence of boundary values of sums of weighted Lp functions defined in wedges. The final result is an application in which we prove a global version of a classical result: namely, the relationship between the global characteristic set of a partial differential operator P and the microglobal wavefront sets of u and Pu. (AU) | |
| FAPESP's process: | 18/02663-0 - Global ultradifferentiable functions, complex analysis, and PDE's |
| Grantee: | Gustavo Hoepfner |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |
| FAPESP's process: | 17/06993-2 - Qualitative theory of PDE's in connexion with harmonic analysis, geometric measure theory and several complex variables |
| Grantee: | Gustavo Hoepfner |
| Support Opportunities: | Scholarships abroad - Research |
| FAPESP's process: | 17/03825-1 - Qualitative properties of PDE' and Several Complex Variables |
| Grantee: | Gustavo Hoepfner |
| Support Opportunities: | Regular Research Grants |