scholarly journals Error bounds on numerical solutions of dirichlet problems for quasilinear elliptic equations

1966 ◽  
Author(s):  
Thurman G. Frank
Keyword(s):  
Error Bounds ◽  
Elliptic Equations ◽  
Numerical Solutions ◽  
Quasilinear Elliptic Equations ◽  
Dirichlet Problems ◽  
Quasilinear Elliptic

Strong Maximum Principle for Some Quasilinear Dirichlet Problems Having Natural Growth Terms

2020 ◽  
Vol 20 (2) ◽  
pp. 503-510
Author(s):  
Lucio Boccardo ◽  
Luigi Orsina
Keyword(s):  
Maximum Principle ◽  
Elliptic Equations ◽  
Strong Maximum Principle ◽  
Quasilinear Elliptic Equations ◽  
Quadratic Growth ◽  
Natural Growth ◽  
Dirichlet Problems ◽  
Natural Growth Terms ◽  
Quasilinear Elliptic ◽  
Lower Order Terms

AbstractIn this paper, dedicated to Laurent Veron, we prove that the Strong Maximum Principle holds for solutions of some quasilinear elliptic equations having lower order terms with quadratic growth with respect to the gradient of the solution.

Comparison results in second order quasilinear Dirichlet problems

1991 ◽  
Vol 118 (1-2) ◽  
pp. 91-103 ◽  
Author(s):  
L. E. Payne ◽  
J. R. L. Webb
Keyword(s):  
Elliptic Equations ◽  
Second Order ◽  
Quasilinear Elliptic Equations ◽  
Dirichlet Problems ◽  
Comparison Results ◽  
Special Cases ◽  
Quasilinear Elliptic ◽  
Comparison Technique

SynopsisIn [6] and [9] two different methods are given for comparing solutions of Dirichlet problems for second order quasilinear elliptic equations on convex regions. In this paper a general comparison technique is outlined—one which contains the methods of [6] and [9] as special cases. This technique is then applied to a number of special examples, comparisons with known results are given and a number of possible extensions are indicated.

scholarly journals Quasilinear Dirichlet Problems with Degenerated p-Laplacian and Convection Term

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 139
Author(s):  
Dumitru Motreanu ◽  
Elisabetta Tornatore
Keyword(s):  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Convection Term ◽  
Bounded Solutions ◽  
Dirichlet Problems ◽  
Abstract Result ◽  
Functional Setting ◽  
Quasilinear Elliptic ◽  
Substantial Change

The paper develops a sub-supersolution approach for quasilinear elliptic equations driven by degenerated p-Laplacian and containing a convection term. The presence of the degenerated operator forces a substantial change to the functional setting of previous works. The existence and location of solutions through a sub-supersolution is established. The abstract result is applied to find nontrivial, nonnegative and bounded solutions.

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