Collaborative Research: L-infinity variational problems and the Aronsson equation

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L-infinity variational problems are problems where one seeks to find the maximum (or minimum) of a functional that is an expression involving the pointwise behavior of a function and its gradient. The study of such problems has become very active recently and this project will support the study of a number of important open questions in the area. A particular interest is the relationship between minimizers of the variational problems and solutions of the corresponding Aronsson equation. Other questions include the uniqueness and regularity of solutions of the Aronsson equations and the characterization of the principal eigenvalue of the infinity-Laplacian operator. These variational problems are not only interesting mathematically but arise in a number of different areas of applications. These include the determination of optimal radiation treatments in chemotherapy, in image analysis and reconstruction and in determining winning strategies in certain types of games. The results obtained under this research will help describe the mathematical models of these applications. This is a collaborative award with Dr Changyou Wang of the University of Kentucky.