Stability and regularity of solutions to elliptic systems of partial differential equations

2007 ◽  
pp. 137-153
Author(s):  
A. P. Kopylov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Elliptic Systems ◽  
Regularity Of Solutions ◽  
Partial Differential

Some Relationships Between Bers and Beltrami Systems and Linear Elliptic Systems of Partial Differential Equations

1965 ◽  
Vol 17 ◽  
pp. 627-642
Author(s):  
W. V. Caldwell
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Elliptic Systems ◽  
Fundamental Importance ◽  
Partial Differential ◽  
Equal Importance

Much work has been done in the investigation of the properties of solutions of linear elliptic systems of partial differential equations. Among these systems, the class of Beltrami systems has been studied for many years and has been shown to be of fundamental importance. Another class, perhaps of equal importance, is the class defined by Bers (1), which the author has taken the liberty of calling Bers systems. Solutions of these systems will be called Beltrami and Bers functions respectively.

An example of H1-unboundedness of solutions to strongly elliptic systems of partial differential equations in a laminated geometry

1987 ◽  
Vol 105 (1) ◽  
pp. 77-82 ◽  
Author(s):  
Hervé Le Dret
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Elliptic Systems ◽  
Boundedness Of Solutions ◽  
Elastic Materials ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Hadamard Condition

SynopsisIn this paper, a counterexample is given to the H1-boundedness of solutions to a sequence of systems of linear partial differential equations uniformly satisfying a strict Legendre–Hadamard condition and whose coefficients depend on one direction only. This counterexample is relevant for the theory of homogenisation of laminated elastic materials.

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