Seventy five (thousand) unsolved problems in analysis and partial differential equations
The author presents a rich collection of worthy open problems concerning various areas in function theory, functional analysis, and the theory of linear and nonlinear partial differential equations. The author, a leader in these fields, provides also concise explanations of the origins and backgrounds of the problems. The problems include the following topics: Sobolev spaces of integer and fractional orders; isoperimetric problems for fractional perimeter; strong capacity inequalities; boundary traces; best constants for some classical inequalities; integral operators and equations; linear and nonlinear elliptic, parabolic and hyperbolic operators; stationary Stokes and Navier-Stokes systems. The extensive bibliography, which, as one would expect, contains many references to the author's own significant contributions to these areas, provides a valuable guide for those who would like to follow the author in his profound study. It seems to the reviewer that Problem 51 of the paper has been solved affirmatively in [\textit{M. Fraas} and \textit{Y. Pinchover}, Confluentes Math. 3, No. 2, 291--323 (2011; Zbl 1227.35107)].
scientific article; zbMATH DE number 6882312
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