scholarly journals Axially symmetric elasticity problems for the hollow cylinder with the stress-free ends. Analytical solving via a variational method of homogeneous solutions

2020 ◽  
Vol 7 (1) ◽  
pp. 48-63
Author(s):  
V. F. Chekurin ◽  
◽  
L. I. Postolaki ◽  
◽  
Keyword(s):  
Variational Method ◽  
Hollow Cylinder ◽  
Axially Symmetric ◽  
Homogeneous Solutions ◽  
Elasticity Problems

scholarly journals On one-homogeneous solutions to elliptic systems with spatial variable dependence in two dimensions

2010 ◽  
Vol 140 (3) ◽  
pp. 449-475 ◽  
Author(s):  
Jonathan J. Bevan
Keyword(s):  
Variational Method ◽  
Elliptic System ◽  
Homogeneous Solution ◽  
Elliptic Systems ◽  
Divergence Form ◽  
Two Dimensions ◽  
Spatial Variable ◽  
Original Result ◽  
Homogeneous Solutions ◽  
Special Case

We extend a result from Phillips by showing that one-homogeneous solutions of certain elliptic systems in divergence form either do not exist or must be affine. The result is novel in two ways. Firstly, the system is allowed to depend (in a sufficiently smooth way) on the spatial variable x. Secondly, Phillips's original result is shown to apply to W one-homogeneous solutions, from which his treatment of Lipschitz solutions follows as a special case. A singular one-homogeneous solution to an elliptic system violating the hypotheses of the main theorem is constructed using a variational method.

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