scholarly journals Effective energy integral functionalsfor thin films on curl-free vector fields in the Orlicz–Sobolev space setting

2019 ◽  
Vol 119 ◽  
pp. 259-277
Author(s):  
Włodzimierz Laskowski ◽  
Hong Thai Nguyen
2013 ◽  
Vol 46 (3) ◽  
Author(s):  
Włodzimierz Laskowski ◽  
Hong Thai Nguyen

AbstractWe consider an elastic thin film as a bounded open subset


2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Toni Heikkinen

Let Φ be anN-function. We show that a functionu∈LΦ(ℝn)belongs to the Orlicz-Sobolev spaceW1,Φ(ℝn)if and only if it satisfies the (generalized) Φ-Poincaré inequality. Under more restrictive assumptions on Φ, an analog of the result holds in a general metric measure space setting.


1994 ◽  
Vol 354 ◽  
Author(s):  
Mandar S. Mudholkar ◽  
Levi T. Thompson

AbstractMolybdenum nitrides are active and selective hydrodenitrogenation (HDN) catalysts. The catalytic properties of molybdenum nitrides were found to be dependent on the structural properties. The purpose of research described in this paper was to synthesize molybdenum nitride thin films with well defined structures and stoichiometries using ion beam assisted deposition. The films were deposited by evaporating Mo metal, and simultaneously bombarding the growing film with low energy nitrogen ions. The phase constituents of the films were determined using x-ray diffraction and the film composition was obtained by Rutherford backscattering spectrometry.The film composition and phase constituents were strong functions of the ion-to-atom arrival rate ratio, ion energy and ion angle of incidence. Differences in the film composition for different arrival rate ratios and ion angles of incidence were interpreted based on reflection and sputtering effects. Our results suggest that phase formation was governed by the effective energy density per deposited atom. Evaluation of the effective energy density per deposited atom and its physical significance in ion beam assisted deposition is discussed.


2010 ◽  
Vol 73 (10) ◽  
pp. 3239-3253 ◽  
Author(s):  
Mihai Mihăilescu ◽  
Gheorghe Moroşanu ◽  
Vicenţiu Rădulescu

2020 ◽  
Vol 127 (24) ◽  
pp. 245704 ◽  
Author(s):  
G. Bridoux ◽  
G. D. Ruano ◽  
J. M. Ferreyra ◽  
M. Villafuerte

Author(s):  
HEPING WANG

In this paper, we study two problems: one is of the worst case cubature error over the Sobolev classes on the sphere and another is of the approximation by hyperinterpolation operators on the sphere in the Sobolev space setting. We obtain lower estimates for the worst case cubature error over the Sobolev classes, which are optimal in the sense of order. We also obtain optimal estimates for the approximation by hyperinterpolation operators on the sphere in the Sobolev space setting.


Sign in / Sign up

Export Citation Format

Share Document