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Smooth Solutions to a Linear System
PDE and Applied Math Seminar| Speaker: | Kevin Luli, UC-Davis |
| Location: | zoom |
| Start time: | Thu, Mar 10 2022, 4:10PM |
Consider the following two problems:
(1) Given a subset E of R^n and a real-valued function f on E, how do we know if f extends to a C^m function on R^n?
(2) Given an MxN matrix A of functions on R^n and a vector-valued functions f from R^n to R^N, how do we know if there exist a C^m solution F such that AF = f?
It turns out (1) and (2) are actually the same problem. Moreover, if (2) has a solution F and A, f are polynomials, then in addition to being C^m, F can be taken to be semialgebraic (a natural generalization of polynomials). This talk draws on joint work with C. Fefferman, F. Jiang, and K. O'Neill.