Análisis no lineal en espacios euclidianos, no euclidianos y aplicaciones
Differential equations appear naturally in Economy, Engineering and Physics. Some mathematical models, such as the Thomas-Fermi energy functional to the quantum study of matter or the Kardar-Parisi-Zhang model to describe the evolution of interfasis, require to solve partial differential equations...
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| Autores principales: | , , , , , , , |
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2019
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| Acceso en línea: | https://bdigital.uncu.edu.ar/fichas.php?idobjeto=14123 |
| Sumario: | Differential equations appear naturally in Economy, Engineering and Physics. Some mathematical models, such as the Thomas-Fermi energy functional to the quantum study of matter or the Kardar-Parisi-Zhang model to describe the evolution of interfasis, require to solve partial differential equations with boundary conditions. In the present research project, we propose to analyse several aspects of the theory of partial differential equations with non-local operators. In particular, we will be interested in the existence, uniqueness and regularity of solutions to problems where the data have minimal regularity assumptions (integrable functions or just measures). Moreover, we will deal different boundary conditions (homogeneous, non-homogeneous, data concentrated on the boundary, etc.) and we will intend to extend the analysis to non-Euclidean spaces as the Heinseberg group and more general Carnot groups. Moreover, the project contemplates the academic formation of human resources (the ending of a Master thesis and the continuation of two PHD thesis), the divulgation of results through expositions and participations in workshops, and the collaboration with research groups from other national and international universities (UBA, Universidad de Granada). Therefore, the current project is going to contribute to the visualization of the Facultad de Ingeniería and the Universidad Nacional de Cuyo in the national and international scientific community. |
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