This National Science Foundation (NSF) Project Grant award provides $253,734 to The Johns Hopkins University to support research on the regularity of solutions to elliptic partial differential equations and generalized minimal submanifolds. The award focuses on two main mathematical objectives: studying unique continuation for solutions to elliptic PDEs and investigating the regularity theory for generalized minimal submanifolds. This research under the NSF's Mathematical and Physical Sciences (CFDA 47.049) program will advance the understanding of physical phenomena governed by elliptic differential equations, such as the shape of bridges, soap bubbles, and drums. The project will also provide professional development opportunities for graduate students through mentoring and a focused learning seminar. This grant is effective from June 1, 2024 through May 31, 2027 and does not involve any planned sub-awards.
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