Solvability of the Dirichlet problem in $H_0^{1,p,\lambda } (\Omega )$ for a class of linear second order elliptic partial differential equations

Equadiff 99 ◽  
2000 ◽  
pp. 609-611
Author(s):  
M. A. Ragusa
Keyword(s):  
Dirichlet Problem ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Elliptic Partial Differential Equations ◽  
Second Order ◽  
Partial Differential

SOLUSI LEMAH MASALAH DIRICHLET PERSAMAAN DIFERENSIAL PARSIAL LINEAR ELIPTIK ORDER DUA

2018 ◽  
Vol 1 (1) ◽  
pp. 1
Author(s):  
Sekar Nugraheni ◽  
Christiana Rini Indrati
Keyword(s):  
Weak Solution ◽  
Dirichlet Problem ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Elliptic Partial Differential Equations ◽  
Second Order ◽  
Partial Differential ◽  
Order Linear ◽  
Definition Of

The weak solution is one of solutions of the partial differential equations, that is generated from derivative of the distribution. In particular, the definition of a weak solution of the Dirichlet problem for second order linear elliptic partial differential equations is constructed by the definition and the characteristics of Sobolev spaces on Lipschitz domain in R^n. By using the Lax Milgram Theorem, Alternative Fredholm Theorem and Maximum Principle Theorem, we derived the sufficient conditions to ensure the uniqueness of the weak solution of Dirichlet problem for second order linear elliptic partial differential equations. Furthermore, we discussed the eigenvalue of Dirichlet problem for second order linear elliptic partial differential equations with  respect to the weak solution.

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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