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| From https://people.math.harvard.edu/~knill/pedagogy/pde/index.html |
5 Sep and 12 Sep
Mathew Gluck
How do researchers in PDEs think about PDEs
Abstract: The classical Poisson problem, say with homogeneous Dirichlet boundary data, seeks to determine which source functions are in the image of the Dirichlet Laplacian. In this talk I will briefly discuss the classical formulation of Poisson’s problem. I will then discuss the modern formulation (i.e., the weak formulation) of this problem in the case that the source is square integrable. Compared to the classical formulation, the modern formulation of Poisson’s problem requires a bit more up-front cost to understand. Specifically, one must (a) carefully specify both the domain and the codomain of the Laplacian and (b) completely overhaul how they understand the Laplacian. However, this extra up-front cost of understanding pays off. Indeed, the existence-uniqueness theory for the modern formulation of Poisson’s problem is much simpler than that for the classical formulation.
Students with interest in PDEs or related topics are especially encouraged to attend.
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