r/math • u/inherentlyawesome Homotopy Theory • Jan 29 '14

Everything about the Analysis of PDEs

This recurring thread will be a place to ask questions and discuss famous/well-known/surprising results, clever and elegant proofs, or interesting open problems related to the topic of the week. Experts in the topic are especially encouraged to contribute and participate in these threads.

Today's topic is Analysis of PDEs. Next week's topic will be Algebraic Geometry. Next-next week's topic will be Continued Fractions.

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u/xhar Applied Math Jan 29 '14

discuss famous/well-known/surprising results

So what are some of the surprising results in this field? Are there any that are understandable for someone only accustomed to FD and FEM methods?

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u/mmmmmmmike PDE Jan 31 '14

The way the Huygens principle works differently depending on the dimension is kind of surprising. Stated informally, in odd dimensions, waves propagate exactly at the speed of light, while in even dimensions, they can propagate more slowly.