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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
Set invariance for differential inclusions applied to PDES?
Your question was essentially answered by the Ph.D. thesis of Dieter Bothe, Multivalued differential equations and graphs and applications, Univ. Paderborn, 1992, see also the comments in the proof of …
4
votes
Accepted
What functions are equal to their symmetric decreasing rearrangement?
It should be straightforward to verify that $\mathcal A$ consists exactly of the lower semi-continuous radial and decreasing functions (which are non-negative and vanish at $\infty$): You already know …