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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
Rellich-Necas identity
My guessing is that the question is about the so-called Rellich-Necas identity, named after the late Czech mathematician Jindrich NECAS. See e.g. [C24], [C14], and [C11] in http://dml.cz/bitstream/h …
2
votes
Connected components of space of maps between two manifolds
For the Sobolev case, I think http://www.lincei.it/pubblicazioni/rendicontiFMN/rol/pdf/M2003-03-14.pdf
may be helpful [together with the references therein].