Many physical models possess the property of being real analytic, while almost none - in fact, none that I know of - possess the property of being smooth but not real analytic. Nonetheless, smoothness is the most common assumption of physical models. One of the reasons for this is the difficulty of fully taking advantage of real analyticity when we have it, whereas smoothness is far easier to handle. This will be an overview talk about what is known in the world of real analyticity, and the tools for proving such results as are known. The central ideas here go back to the late 1950's with work of Cartan (the younger), and Whitney and Bruhat. However, these ideas have not really made their way to the applied community.
Last Updated: Sat Oct 20 17:47:21 2018