scholarly journals Regularity of weak solutions to obstacle problems for nondiagonal quasilinear degenerate elliptic systems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Guangwei Du ◽  
Kelei Zhang ◽  
Yan Dong
Keyword(s):  
Weak Solutions ◽  
Elliptic Systems ◽  
Obstacle Problems ◽  
Regularity Of Weak Solutions ◽  
Degenerate Elliptic

scholarly journals Existence via regularity of solutions for elliptic systems and saddle points of functionals of the calculus of variations

2017 ◽  
Vol 6 (2) ◽  
pp. 99-120 ◽  
Author(s):  
Lucio Boccardo ◽  
Luigi Orsina
Keyword(s):  
Calculus Of Variations ◽  
Weak Solutions ◽  
Saddle Points ◽  
Elliptic Systems ◽  
Regularity Of Solutions ◽  
Integral Functionals ◽  
Content Type ◽  
The Core ◽  
Regularity Of Weak Solutions

AbstractThe core of this paper concerns the existence (via regularity) of weak solutions in ${W_{0}^{1,2}}$ of a class of elliptic systems such as$\left\{\begin{aligned} \displaystyle-\operatorname{div}((A+\varphi)\nabla u)&% \displaystyle=f,\\ \displaystyle-\operatorname{div}(M(x)\nabla\varphi)&\displaystyle=\frac{1}{2}% \lvert\nabla u\rvert^{2},\end{aligned}\right.$deriving from saddle points of integral functionals of the type$J(v,\psi)=\frac{1}{2}\int_{\Omega}(A+\psi_{+})\lvert\nabla v\rvert^{2}-\frac{1% }{2}\int_{\Omega}M(x)\nabla\psi\nabla\psi-\int_{\Omega}fv.$

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