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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.
2
votes
Accepted
An acting condition for a superposition operator from $H^1(\Omega)$ to $H^1(\Omega)$
The following is stated in the paper
Moshe Marcus and Victor J. Mizel, MR 531975 Complete characterization of functions which act, via superposition, on Sobolev spaces, Trans. Amer. Math. Soc. 251 (1 …
2
votes
Accepted
Numerical analysis of parabolic obstacle problem
There's an overview of available schemes in chapter III of
Roland Glowinski, MR 737005 Numerical methods for nonlinear variational problems, ISBN: 0-387-12434-9.
(of which there is also reprint from …