Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/13154
Title: An introduction to the study of critical points of solutions of elliptic and parabolic equations
Authors: Magnanini, Rolando
Keywords: Elliptic partial differential equationsparabolic partial differential equationscritical points of solutionshot spots
Issue Date: 2016
Publisher: EUT Edizioni Università di Trieste
Series/Report no.: Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics
48 (2016)
Abstract: 
We give a survey at an introductory level of old and recent results in the study of critical points of solutions of elliptic and parabolic partial differential equations. To keep the presentation simple, we mainly consider four exemplary boundary value problems: the Dirichlet problem for the Laplace’s equation; the torsional creep prob-lem; the case of Dirichlet eigenfunctions for the Laplace’s equation; the initial-boundary value problem for the heat equation. We shall mostly address three issues: the estimation of the local size of the critical set; the dependence of the number of critical points on the boundary values and the geometry of the domain; the location of critical points in the domain.
Type: Article
URI: http://hdl.handle.net/10077/13154
ISSN: 0049-4704
eISSN: 2464-8728
DOI: 10.13137/2464-8728/13154
Appears in Collections:Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics vol.48 (2016)

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