scholarly journals A non linear approximation method for solving high dimensional partial differential equations: Application in finance

2018 ◽  
Vol 143 ◽  
pp. 14-34
Author(s):  
José Infante Acevedo ◽  
Tony Lelièvre
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Linear Approximation ◽  
Approximation Method ◽  
High Dimensional ◽  
Partial Differential ◽  
Linear Approximation Method ◽  
Non Linear

On the Dirichlet problem for weakly non-linear elliptic partial differential equations

1977 ◽  
Vol 76 (4) ◽  
pp. 283-300 ◽  
Author(s):  
E. N. Dancer
Keyword(s):  
Dirichlet Problem ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Existence Of Solutions ◽  
Elliptic Partial Differential Equations ◽  
Partial Differential ◽  
Weakly Nonlinear ◽  
Partial Derivatives ◽  
Nonlinear Elliptic ◽  
Non Linear

SynopsisWe study the existence of solutions of the Dirichlet problem for weakly nonlinear elliptic partial differential equations. We only consider cases where the nonlinearities do not depend on any partial derivatives. For these cases, we prove the existence of solutions for a wide variety of nonlinearities.

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