On variational problems and nonlinear elliptic equations with nonstandard growth conditions

2011 ◽  
Vol 173 (5) ◽  
pp. 463-570 ◽  
Author(s):  
V. V. Zhikov
Keyword(s):  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Variational Problems ◽  
Growth Conditions ◽  
Nonstandard Growth ◽  
Nonlinear Elliptic ◽  
Nonstandard Growth Conditions

Global gradient estimates for elliptic equations of p(x)-Laplacian type with BMO nonlinearity

2016 ◽  
Vol 2016 (715) ◽  
pp. 1-38 ◽  
Author(s):  
Sun-Sig Byun ◽  
Jihoon Ok ◽  
Seungjin Ryu
Keyword(s):  
Weak Solution ◽  
Elliptic Problem ◽  
Elliptic Equations ◽  
Growth Conditions ◽  
Divergence Form ◽  
Gradient Estimates ◽  
Nonlinear Elliptic Problem ◽  
Nonstandard Growth ◽  
Nonlinear Elliptic ◽  
Nonstandard Growth Conditions

AbstractWe consider a nonlinear elliptic problem in divergence form, with nonstandard growth conditions, on a bounded domain. We obtain the global Calderón–Zygmund type gradient estimates for the weak solution of such a problem in the setting of Lebesgue and Sobolev spaces with variable

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