Necessary conditions for minimax control problems of second order elliptic partial differential equations
type: Item
instance of: scholarly article
title: Necessary conditions for minimax control problems of second order elliptic partial differential equations
zbMATH Open document ID: 0802.49016
published in: Kodai Mathematical Journal
publication date: 1994-04-28T00:00:00Z
full work available at URL: http://purl.umn.edu/2401
review text: The paper discusses the problem of the minimizing of \(\text{ess}_{x\in \Omega} \sup h(x,y(u; x), u(x))\) over all pairs \((y,u)\) satisfying \(\Delta u= f(x, y(x), u(x))\), \(x\in \Omega\), \(y\mid_{\partial \Omega} =0\), with additional constraints on the \(y\) (for instance, \(y(x_ i) =a_ i\), \(i=1,\dots, m)\). Under some regularity and growth conditions on the functions \(h\) and \(f\) and some general assumptions on the structure of the problem the author proves an analogue of the Pontryagin's maximum principle.
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 35J85
Mathematics Subject Classification ID: 49K35
zbMATH DE Number: 558891
zbMATH Keywords: minimax problem
zbMATH Keywords: Pontryagin's maximum principle
author: Jiongmin Yong
reviewed by: Uldis Raitums
MaRDI profile type: Publication
OpenAlex ID: W2016408881
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DOI: 10.2996/KMJ/1138039853
description: scientific article; zbMATH DE number 558891