The Dirichlet Problem for Nonlinear Elliptic Equations: A Hilbert Space Approach

1975 ◽  
pp. 43-64
Author(s):  
Djairo Guedes de Figueiredo
Keyword(s):  
Hilbert Space ◽  
Dirichlet Problem ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Nonlinear Elliptic ◽  
Space Approach

Existence results for the Dirichlet problem of some degenerate nonlinear elliptic equations

2014 ◽  
Vol 20 (2) ◽  
Author(s):  
Albo Carlos Cavalheiro
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Nonlinear Elliptic Equations ◽  
Existence Results ◽  
Uniqueness Of Solutions ◽  
Nonlinear Elliptic

AbstractIn this paper we are interested in the existence and uniqueness of solutions for the Dirichlet problem associated to the degenerate nonlinear elliptic equations

scholarly journals Existence Results For A Class Of Nonlinear Degenerate Elliptic Equations

2019 ◽  
Vol 5 (2) ◽  
pp. 164-178
Author(s):  
Albo Carlos Cavalheiro
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Weighted Sobolev Spaces ◽  
Nonlinear Elliptic Equations ◽  
Existence Results ◽  
Degenerate Elliptic Equations ◽  
Nonlinear Elliptic ◽  
Degenerate Elliptic ◽  
Nonlinear Degenerate

AbstractIn this paper we are interested in the existence of solutions for Dirichlet problem associated with the degenerate nonlinear elliptic equations\left\{ {\matrix{ { - {\rm{div}}\left[ {\mathcal{A}\left( {x,\nabla u} \right){\omega _1} + \mathcal{B}\left( {x,u,\nabla u} \right){\omega _2}} \right] = {f_0}\left( x \right) - \sum\limits_{j = 1}^n {{D_j}{f_j}\left( x \right)\,\,{\rm{in}}} \,\,\,\,\,\Omega ,} \hfill \cr {u\left( x \right) = 0\,\,\,\,{\rm{on}}\,\,\,\,\partial \Omega {\rm{,}}} \hfill \cr } } \right.in the setting of the weighted Sobolev spaces.

Aprioribounds for a class of nonlinear elliptic equations and applications to physical problems

1981 ◽  
Vol 88 (1-2) ◽  
pp. 75-81 ◽  
Author(s):  
Catherine Bandle
Keyword(s):  
Dirichlet Problem ◽  
Lower Bounds ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Upper And Lower Bounds ◽  
Two Dimensional ◽  
Nonlinear Dirichlet Problem ◽  
Nonlinear Elliptic ◽  
Physical Problems ◽  
Maximal Pressure

SynopsisUpper and lower bounds for the solutions of a nonlinear Dirichlet problem are given and isoperimetric inequalities for the maximal pressure of an ideal charged gas are constructed. The method used here is based on a geometrical result for two-dimensional abstract surfaces.

scholarly journals Existence and uniqueness of solutions for a semilinear elliptic system

2005 ◽  
Vol 2005 (10) ◽  
pp. 1507-1523 ◽  
Author(s):  
Robert Dalmasso
Keyword(s):  
Dirichlet Problem ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Biharmonic Equation ◽  
Nonlinear Elliptic Equations ◽  
Uniqueness Of Solutions ◽  
Nonlinear Elliptic ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic System ◽  
Homogeneous Dirichlet Problem

We consider the existence, the nonexistence, and the uniqueness of solutions of some special systems of nonlinear elliptic equations with boundary conditions. In a particular case, the system reduces to the homogeneous Dirichlet problem for the biharmonic equationΔ2u=|u|pin a ball withp>0.

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