Seventy five (thousand) unsolved problems in analysis and partial differential equations
type: Item
instance of: scholarly article
title: Seventy five (thousand) unsolved problems in analysis and partial differential equations
zbMATH Open document ID: 1398.35019
published in: Integral Equations and Operator Theory
publication date: 2018-06-08T00:00:00Z
review text: 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)].
reviewed by: Yehuda Pinchover
Mathematics Subject Classification ID: 35Jxx
Mathematics Subject Classification ID: 35Kxx
Mathematics Subject Classification ID: 35Lxx
Mathematics Subject Classification ID: 45-XX
Mathematics Subject Classification ID: 46Exx
Mathematics Subject Classification ID: 35-02
Mathematics Subject Classification ID: 45-02
Mathematics Subject Classification ID: 46-02
zbMATH DE Number: 6882312
zbMATH Keywords: linear and nonlinear elliptic operators
zbMATH Keywords: parablic operators
zbMATH Keywords: hyperbolic operators
zbMATH Keywords: integral operators
zbMATH Keywords: Stokes and Navier-Stokes systems
zbMATH Keywords: Sobolev spaces
author: V. Maz'ya
MaRDI profile type: Publication
full work available at URL: s00020-018-2460-8
OpenAlex ID: W2801721719
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Seventy five (thousand) unsolved problems in analysis and partial differential equations (Wikidata QID)
Wikidata QID: Q129908322

Seventy five (thousand) unsolved problems in analysis and partial differential equations (DOI)
DOI: 10.1007/S00020-018-2460-8

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