scholarly journals Local boundedness of variational solutions to evolutionary problems with non-standard growth

2016 ◽  
Vol 23 (2) ◽  
Author(s):  
Thomas Singer
Keyword(s):  
Local Boundedness ◽  
Variational Solutions

Comparison of Variational Solutions of the Thomas-Fermi Model in Terms of the Corrected Ionization Energy

1987 ◽  
Vol 42 (9) ◽  
pp. 943-947
Author(s):  
I. Agil ◽  
A. Alharkan ◽  
H . Alhendi ◽  
A. Alnaghmoosh
Keyword(s):  
Ionization Energy ◽  
Trial Function ◽  
Binding Energies ◽  
Initial Slope ◽  
Fermi Model ◽  
Thomas Fermi ◽  
Variational Solutions ◽  
Comparison Of The Results

It is shown that leading corrections, to the ionization energy, of many-electrons atom, can be expressed as leading corrections of initial slope of trial variational solutions of the Thomas-Fermi equation. Some variational solutions with different initial slopes are compared. A comparison of the results shows, that as far as the binding energies are concerned a trial function with its slope not close to the (negative) Baker’s constant may not be suited.

Local boundedness of minimizers in a limit case

1990 ◽  
Vol 69 (1) ◽  
pp. 19-25 ◽  
Author(s):  
Nicola Fusco ◽  
Carlo Sbordone
Keyword(s):  
Limit Case ◽  
Local Boundedness

Some Mixed Boundary-Value Problems of the Semi-Infinite Strip

1957 ◽  
Vol 24 (2) ◽  
pp. 261-268
Author(s):  
G. Horvay ◽  
J. S. Born
Keyword(s):  
Shear Stress ◽  
Boundary Value Problems ◽  
Approximate Method ◽  
Normal Stress ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Normal Displacement ◽  
Infinite Strip ◽  
Elastic Strip ◽  
Variational Solutions

Abstract Rigorous and approximate (variational) solutions are given for the semi-infinite elastic strip, traction-free along the long edges, when the short edge is subjected (a) to a quadratic shear displacement, zero normal stress, (b) to a cubic normal displacement, zero shear stress. The approximate method of self-equilibrating functions is extended.

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.

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