scholarly journals On a method for constructing Bergman kernels

1980 ◽  
Vol 29 (4) ◽  
pp. 454-461
Author(s):  
A. Azzam ◽  
E. Kreyszig
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Second Order ◽  
Partial Differential ◽  
Bergman Kernels ◽  
Order Linear ◽  
Independent Variables ◽  
New Class ◽  
Linear Partial Differential Equations ◽  
Two Independent Variables

AbstractWe establish a method of constructing kernels of Bergman operators for second-order linear partial differential equations in two independent variables, and use the method for obtaining a new class of Bergman kernels, which we call modified class E kernels since they include certain class E kernals. They also include other kernels which are suitable for global representations of solutions (whereas Bergman operators generally yield only local representations).

scholarly journals On the Solution of Non-linear Partial Differential Equations of the Second Order

1891 ◽  
Vol 10 ◽  
pp. 63-70
Author(s):  
John M'Cowan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Second Order ◽  
Partial Differential ◽  
Independent Variables ◽  
Linear Partial Differential Equations ◽  
General Utility ◽  
Non Linear ◽  
Two Independent Variables

§ 1. It is proposed to discuss in this paper partial differential equations involving two independent variables x and y, and a dependent variable z. The method of reduction which is explained can be applied to certain equations involving more than two independent variables, but such application is subject to too many restrictions to be of much general utility.

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