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Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
8
votes
Why can't there be a general theory of nonlinear PDE?
this is a comment to Deane Yang, but apparently it was too long so here is a separate answer. My background is in numerical solution of PDEs
1) while I know about this, it is not at all well-known by …
5
votes
Green's formula for nonorientable manifolds
So it seems that Bott & Tu are saying that orientability doesn't really matter: Stokes theorem remains valid if one replaces forms by densities. But then it's curious why this fact is not clearly stat …
10
votes
Why can't there be a general theory of nonlinear PDE?
I think there is something you can call a general theory of PDEs. It started already long time ago with Meray, Riquier, Janet, Elie Cartan. There is an important survey article by Donald Spencer: Over …