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

Local Solvability in L 2 of First Order Linear PDEs

1970 ◽  
Vol 92 (2) ◽  
pp. 369 ◽  
Author(s):  
Francois Treves
Keyword(s):  
Local Solvability ◽  
Order Linear ◽  
First Order ◽  
Linear Pdes

scholarly journals On first order linear PDE systems all of whose solutions are harmonic functions

2006 ◽  
Vol 30 (1) ◽  
pp. 149-170 ◽  
Author(s):  
Sorin Dragomir ◽  
Ermanno Lanconelli
Keyword(s):  
Harmonic Functions ◽  
Order Linear ◽  
First Order ◽  
Linear Pde ◽  
Pde Systems

scholarly journals Local Solvability of First Order Linear Operators with Lipschitz Coefficients in Two Variables

1995 ◽  
Vol 121 (2) ◽  
pp. 406-416 ◽  
Author(s):  
J. Hounie ◽  
M. Eulalia ◽  
M. Melo
Keyword(s):  
Local Solvability ◽  
Linear Operators ◽  
Order Linear ◽  
First Order

scholarly journals Explicit Runge–Kutta Schemes and Finite Elements with Symmetric Stabilization for First-Order Linear PDE Systems

2010 ◽  
Vol 48 (6) ◽  
pp. 2019-2042 ◽  
Author(s):  
Erik Burman ◽  
Alexandre Ern ◽  
Miguel A. Fernández
Keyword(s):  
Finite Elements ◽  
Order Linear ◽  
First Order ◽  
Linear Pde ◽  
Pde Systems ◽  
Runge Kutta

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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