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A survey of topics in analysis and partial differential equations. (English) Zbl 1228.35006

This is a survey paper focused on various topics presented in recent publications on partial differential equations. It covers topics arising in linear or nonlinear evolution equations of first or second order in the time-variable, linear and nonlinear elliptic equations, spectral properties, singular perturbations, formation of layers, and spaces of functions, in particular of BMO, Sobolev, and UMD type. The article can be used as a dictionary. Its aim is to provide guidance for young researchers in mathematics and applied sciences, biology, chemistry, mechanics and physics. Contents: Attractor to Fokker-Planck equation; Aubry-type sets; BMO and related spaces; Cahn-Hilliard-Gurtin equation; Dimensions in a metric space; Dirac operator; Douglis-Nirenberg elliptic systems; Fokker-Planck equation; Gierer-Meinhardt system; Wavefront sets; Gray-Scott systems; Kirchoff-type equations; Martingale difference sequences; Maximal regularity.

MSC:

35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
35B41 Attractors
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