On the local solvability of certain overdetermined systems of first-order linear PDE

1992 ◽  
Vol 59 (1) ◽  
pp. 225-230
Author(s):  
François Treves
Keyword(s):  
Local Solvability ◽  
Order Linear ◽  
First Order ◽  
Overdetermined Systems ◽  
Linear Pde

scholarly journals Local Solvability inLpof First-Order Linear Operators

1996 ◽  
Vol 197 (1) ◽  
pp. 42-53 ◽  
Author(s):  
Jorge Hounie ◽  
Eduardo Perdigão de Lemos
Keyword(s):  
Local Solvability ◽  
Linear Operators ◽  
Order Linear ◽  
First Order

scholarly journals Two scale defect measure and linear equations with oscillating coefficients

Filomat ◽  
2019 ◽  
Vol 33 (9) ◽  
pp. 2867-2873
Author(s):  
Jelena Aleksic ◽  
Stevan Pilipovic
Keyword(s):  
Linear Equations ◽  
Convergent Sequence ◽  
Dimensional Torus ◽  
Strong Limit ◽  
Absolutely Continuous ◽  
Order Linear ◽  
First Order ◽  
Linear Pde ◽  
Defect Measure ◽  
Oscillating Coefficients

Microlocal measure ? is associated to a two-scale convergent sequence un over Rd with the limit u ? L2(Rd x Td), Td is a torus, to analyze possible strong limit. ? is an operator valued measure absolutely continuous with respect to the product of scalar microlocal defect measure and a measure on the d-dimensional torus. The result is applied to the first order linear PDE with the oscillating coefficients.

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