scholarly journals A Resonance Problem for Non-Local Elliptic Operators

2013 ◽  
Vol 32 (4) ◽  
pp. 411-431 ◽  
Author(s):  
Alessio Fiscella ◽  
Raffaella Servadei ◽  
Enrico Valdinoci
Keyword(s):  
Elliptic Operators ◽  
Resonance Problem ◽  
Non Local

scholarly journals On some noncoercive variational inequalities containing degenerate elliptic operators

2003 ◽  
Vol 44 (3) ◽  
pp. 409-430
Author(s):  
Vy Khoi Le
Keyword(s):  
Boundary Conditions ◽  
Variational Inequalities ◽  
Elliptic Operators ◽  
Existence Results ◽  
Resonance Problem ◽  
Solution Existence ◽  
Degenerate Elliptic Operators ◽  
Degenerate Elliptic ◽  
Noncoercive Variational Inequalities

AbstractWe are concerned with the solvability of variational inequalities that contain degenerate elliptic operators. By using a recession approach, we find conditions on the boundary conditions such that the inequality has at least one solution. Existence results of Landesman-Lazer type for a nonsmooth inequality and a resonance problem for a weighted p-Laplacian are discussed in detail.

Toward High-Resolution Low-Voltage SEM

1988 ◽  
Vol 46 ◽  
pp. 218-219
Author(s):  
Zhifeng Shao
Keyword(s):  
Low Voltage ◽  
Spherical Aberration ◽  
Chromatic Aberration ◽  
Limiting Factor ◽  
Operating Voltage ◽  
Probe Radius ◽  
Non Local ◽  
Electron Microscopes ◽  
Image Position ◽  
Scanning Electron Microscopes

Recently, low voltage (≤5kV) scanning electron microscopes have become popular because of their unprecedented advantages, such as minimized charging effects and smaller specimen damage, etc. Perhaps the most important advantage of LVSEM is that they may be able to provide ultrahigh resolution since the interaction volume decreases when electron energy is reduced. It is obvious that no matter how low the operating voltage is, the resolution is always poorer than the probe radius. To achieve 10Å resolution at 5kV (including non-local effects), we would require a probe radius of 5∽6 Å. At low voltages, we can no longer ignore the effects of chromatic aberration because of the increased ratio δV/V. The 3rd order spherical aberration is another major limiting factor. The optimized aperture should be calculated as

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