William is a third-year student at USyd majoring in Pure Mathematics. He wishes to pursue a career in academia with his primary interests in the confluence of PDE and Geometry. His hobbies include gaming, reading, fishing and cricket.
Powers of Maximal Monotone Operators
If A is a mapping from a vector space H into H, the positive integer powers of A are well understood as the composition of two mappings. In this project, we want to find an appropriate definition of kth powers of A (k greater than or equal to 1), of possibly multivalued mappings which map from a Hilbert space H into the power set P(H). The case k=2 has been studied in a paper by Benilan and Alraabious. Thus, our task will be to discover the case for powers greater than or equal to 3 and also the case for non-integer powers greater than 1. We will also study the impact of taking powers of operators on the corresponding first-order evolution problem.