Geometric Properties for Parabolic and Elliptic PDEs
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Geometric Properties for Parabolic and Elliptic PDE's
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You submitted the following rating and review. We'll publish them on our site once we've reviewed them. Three explicit problems that will be studied are the 1 the location of extrema and critical points, 2 the geometry of level sets and 3 the geometry of eigenfunctions of an elliptic operator. The main types of applications will be 4 the analysis of spectral methods on graphs and 5 localization phenomena in mathematical physics.
The main tools will be basic facts from geometry analysis to reinterpret analytic estimates geometrically and vice versa, the interpretation of elliptic equations as fixed points in time of an associated parabolic equation as well as associated techniques from parabolic equations and various aspects of spectral theory. Tools from the discrete world may be useful when reducing estimates to toy models in the graph setting.
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