A simplified proof of a theorem of J. Bourgain on the extension of operators

1989 ◽  
Vol 44 (6) ◽  
pp. 849-851
Author(s):  
S. V. Kislyakov
Keyword(s):  
Extension Of Operators

The Problem on Dynamical Loading of Plane Elastic Regions With Irregular Boundaries

1998 ◽  
Vol 65 (2) ◽  
pp. 476-478
Author(s):  
N. Morozov ◽  
I. Sourovtsova
Keyword(s):  
Wave Propagation ◽  
Boundary Conditions ◽  
The Body ◽  
Single Type ◽  
Edge Condition ◽  
Special Boundary ◽  
Elastic Wedge ◽  
Surface Loading ◽  
Special Surface ◽  
Extension Of Operators

The study of the problem of wave propagation in elastic wedge meets considerable difficulties, which are intensified by the presence of waves of two types that interact with each other through boundary conditions. However, some special surface loading permits separation of the potentials in the boundary conditions, but even in this case the problem cannot be simply reduced to two acoustic ones. The reason for this is that the edge condition cannot be satisfied if the disturbances are limited to a single type (longitudinal or shear). In spite of this the problem, such a special boundary loading nevertheless turns out to be very similar to the acoustic one, which makes it possible to find a closed analytical solution by means of the modified Kostrov method (Kostrov, 1966) and the idea of extension of operators. A similar approach is used for the study of the general problem of loading of the body with several angles.

Optimal Domain and Integral Extension of Operators

2008 ◽  
Author(s):  
Susumu Okada ◽  
Werner J. Ricker ◽  
Enrique A. Sánchez Pérez
Keyword(s):  
Optimal Domain ◽  
Integral Extension ◽  
Extension Of Operators
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