scholarly journals Well-Posedness Results for Anisotropic Nonlinear Elliptic Equations with Variable Exponent and L¹-Data

Cubo (Temuco) ◽  
2010 ◽  
Vol 12 (1) ◽  
pp. 133-148 ◽  
Author(s):  
Stanislas Ouaro
Keyword(s):  
Elliptic Equations ◽  
Variable Exponent ◽  
Nonlinear Elliptic Equations ◽  
Well Posedness ◽  
Nonlinear Elliptic

scholarly journals On a Class of Anisotropic Nonlinear Elliptic Equations with Variable Exponent

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Guoqing Zhang ◽  
Hongtao Zhang
Keyword(s):  
Weak Solution ◽  
Elliptic Equations ◽  
Existence And Uniqueness ◽  
Variable Exponent ◽  
Nonlinear Elliptic Equations ◽  
Nonlinear Elliptic ◽  
Priori Estimates

Based on truncation technique and priori estimates, we prove the existence and uniqueness of weak solution for a class of anisotropic nonlinear elliptic equations with variable exponentp(x)→growth. Furthermore, we also obtain that the weak solution is locally bounded and regular; that is, the weak solution isLloc∞(Ω)andC1,α(Ω).

scholarly journals Nontrivial Solution for a Nonlocal Elliptic Transmission Problem in Variable Exponent Sobolev Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
Bilal Cekic ◽  
Rabil A. Mashiyev
Keyword(s):  
Nontrivial Solution ◽  
Sobolev Spaces ◽  
Elliptic Equations ◽  
Variable Exponent ◽  
Nonlinear Elliptic Equations ◽  
Transmission Problem ◽  
Variational Techniques ◽  
Nonlinear Elliptic ◽  
Variable Exponent Sobolev Spaces ◽  
Nonstandard Growth Condition

In this paper, by means of adequate variational techniques and the theory of the variable exponent Sobolev spaces, we show the existence of nontrivial solution for a transmission problem given by a system of two nonlinear elliptic equations ofp(x)-Kirchhoff type with nonstandard growth condition.

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