First order linear partial differential equations with discontinuous coefficients

1981 ◽  
Vol 128 (1) ◽  
pp. 325-340 ◽  
Author(s):  
Luciano de Simon ◽  
Giovanni Torelli
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Discontinuous Coefficients ◽  
Partial Differential ◽  
Order Linear ◽  
First Order ◽  
Linear Partial Differential Equations

scholarly journals First-order linear partial differential equations in the class of separately differentiable functions

2013 ◽  
Vol 5 (1) ◽  
pp. 89-93
Author(s):  
V.I. Myronyk ◽  
V.V. Mykhaylyuk
Keyword(s):  
Partial Differential Equations ◽  
General Solution ◽  
Differential Equations ◽  
Partial Differential ◽  
Order Linear ◽  
First Order ◽  
Linear Partial Differential Equations ◽  
Differentiable Functions

It is obtained a general solution of first-order linear partial differential equations in the class of separately differentiable functions.

scholarly journals WARD IDENTITIES FOR AFFINE-VIRASORO CORRELATORS

1994 ◽  
Vol 09 (02) ◽  
pp. 265-311 ◽  
Author(s):  
M.B. HALPERN ◽  
N.A. OBERS
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Nonlinear Equations ◽  
Matrix Factorization ◽  
Ward Identities ◽  
Partial Differential ◽  
Order Linear ◽  
First Order ◽  
Linear Partial Differential Equations ◽  
Abstract Level

Generalizing the Knizhnik-Zamolodchikov equations, we derive a hierarchy of nonlinear Ward identities for affine-Virasoro correlators. The hierarchy follows from null states of the Knizhnik-Zamolodchikov type and the assumption of factorization, whose consistency we verify at an abstract level. Solution of the equations requires concrete factorization ansätze, which may vary over affine-Virasoro space. As a first example, we solve the nonlinear equations for the coset constructions, using a matrix factorization. The resulting coset correlators satisfy first-order linear partial differential equations whose solutions are the coset blocks defined by Douglas.

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