RaDiCHAPDE
Financiado
Rectifiability and Density in Carnot and Homogeneous Groups, and Applications to...
Rectifiability and Density in Carnot and Homogeneous Groups, and Applications to Partial Differential Equations
The core of this project is Geometric Measure Theory (GMT) in Homogeneous Groups. The PI suggests exploring exciting original research avenues regarding the interplay between the concepts of flatness, density, and regularity of me...
The core of this project is Geometric Measure Theory (GMT) in Homogeneous Groups. The PI suggests exploring exciting original research avenues regarding the interplay between the concepts of flatness, density, and regularity of measures, and their applications to the theory of Partial Differential Equations (PDEs) and Free Boundary Problems (FBPs) in non-Euclidean spaces. The project’s potential for groundbreaking discovery is achieved by focusing on the investigation of i) the extension of the very classical density problem, whose solution in Euclidean spaces is codified in the celebrated Preiss' rectifiability theorem, to parabolic and Kolmogorov spaces; ii) the quantitative Reifenberg Theorem for measures in the parabolic space and quantitative dimensional estimates of the mutual singular set for the caloric measure in a two-phase problem; iii) the interplay between differentiability of Lipschitz functions and fine geometric properties of Radon measures in general Homogeneous Groups. As a byproduct of the study of iii), it will be obtained a converse to Pansu's Differentiability Theorem.
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Duración del proyecto: 26 meses
Fecha Inicio: 2022-07-18
Fecha Fin: 2024-09-30
Fecha Fin: 2024-09-30
Línea de financiación: concedida
El organismo HORIZON EUROPE notifico la concesión del proyecto el día 2024-09-30
Línea de financiación objetivo
El proyecto se financió a través de la siguiente ayuda:
HORIZON-MSCA-2021-PF-01-01:
MSCA Postdoctoral Fellowships 2021
Cerrada
hace 3 años
Presupuesto
El presupuesto total del proyecto asciende a
165K€
Líder del proyecto
UNIVERSIDAD DEL PAIS VASCO/EUSKAL HERRIKO UNI...
No se ha especificado una descripción o un objeto social para esta compañía.
Total investigadores
45
Total investigadores
45