This $291,367 Project Grant award from the National Science Foundation's (NSF) Division of Mathematical Sciences (CFDA 47.049 - Mathematical and Physical Sciences) supports research by the University of Pennsylvania on several mathematical problems related to partial differential equations, function spaces, and optimization theory. The key work includes:
Studying Morrey's inequality and extending it to Hardy-type inequalities with region constraints, investigating the pressureless Euler system in cosmology to establish solution uniqueness and long-time behavior, and developing optimization theory for semipermeable obstacle problems involving Hamilton-Jacobi equations and minimal surfaces. The grant also provides funding for mentoring a postdoctoral scholar and disseminating research findings to the broader scientific community. This project aims to advance mathematical analysis with potential applications in physics, engineering, and other disciplines. The award period runs from July 1, 2024 to June 30, 2027.
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