Metric Slope and Subdifferential Calculus in Pp(X)

2005 ◽  
pp. 227-278
Keyword(s):  
Subdifferential Calculus

Pareto Subdifferential Calculus for Convex Vector Mappings and Applications to Vector Optimization

2009 ◽  
Vol 19 (4) ◽  
pp. 1970-1994 ◽  
Author(s):  
Mounir El Maghri ◽  
Mohamed Laghdir
Keyword(s):  
Vector Optimization ◽  
Subdifferential Calculus

scholarly journals Subdifferential Calculus Rules in Convex Analysis: A Unifying Approach Via Pointwise Supremum Functions

2008 ◽  
Vol 19 (2) ◽  
pp. 863-882 ◽  
Author(s):  
A. Hantoute ◽  
M. A. López ◽  
C. Zălinescu
Keyword(s):  
Convex Analysis ◽  
Subdifferential Calculus ◽  
Calculus Rules

scholarly journals Hyperbolic Maxwell variational inequalities of the second kind

2020 ◽  
Vol 26 ◽  
pp. 34 ◽  
Author(s):  
Irwin Yousept
Keyword(s):  
Variational Inequalities ◽  
Existence Result ◽  
Semigroup Theory ◽  
Regularity Property ◽  
Well Posedness ◽  
Test Functions ◽  
Local Boundedness ◽  
Subdifferential Calculus ◽  
Faraday’S Law ◽  
Yosida Regularization

We analyze a class of hyperbolic Maxwell variational inequalities of the second kind. By means of a local boundedness assumption on the subdifferential of the underlying nonlinearity, we prove a well-posedness result, where the main tools for the proof are the semigroup theory for Maxwell’s equations, the Yosida regularization and the subdifferential calculus. The second part of the paper focuses on a more general case omitting the local boundedness assumption. In this case, taking into account more regular initial data and test functions, we are able to prove a weaker existence result through the use of the minimal section operator associated with the Nemytskii operator of the governing subdifferential. Eventually, we transfer the developed well-posedness results to the case involving Faraday’s law, which in particular allows us to improve the regularity property of the electric field in the weak existence result.

Extensions Of Subdifferential Calculus Rules in Banach Spaces

1996 ◽  
Vol 48 (4) ◽  
pp. 834-848 ◽  
Author(s):  
A. Jourani ◽  
L. Thibault
Keyword(s):  
Banach Spaces ◽  
Clarke Subdifferential ◽  
Subdifferential Calculus ◽  
Finite Dimensional ◽  
Calculus Rules ◽  
Approximate Subdifferential ◽  
The Clarke Subdifferential

AbstractThis paper is devoted to extending formulas for the geometric approximate subdifferential and the Clarke subdifferential of extended-real-valued functions on Banach spaces. The results are strong enough to include completely the finite dimensional setting.

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