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 problem; 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.
An introduction to the study of critical points of solutions of elliptic and parabolic equations / Magnanini, Rolando. - In: RENDICONTI DELL'ISTITUTO DI MATEMATICA DELL'UNIVERSITÀ DI TRIESTE. - ISSN 0049-4704. - STAMPA. - 48:(2016), pp. 121-166. [10.13137/2464-8728/13154]
An introduction to the study of critical points of solutions of elliptic and parabolic equations
MAGNANINI, ROLANDO
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 problem; 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.File | Dimensione | Formato | |
---|---|---|---|
ReprintRIMUT.pdf
accesso aperto
Descrizione: Articolo principale
Tipologia:
Pdf editoriale (Version of record)
Licenza:
Tutti i diritti riservati
Dimensione
671.05 kB
Formato
Adobe PDF
|
671.05 kB | Adobe PDF |
I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.