Existence via regularity of solutions for elliptic systems and saddle points of functionals of the calculus of variations
2017 ◽
Vol 6
(2)
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pp. 99-120
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Keyword(s):
The Core
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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$J(v,\psi)=\frac{1}{2}\int_{\Omega}(A+\psi_{+})\lvert\nabla v\rvert^{2}-\frac{1% }{2}\int_{\Omega}M(x)\nabla\psi\nabla\psi-\int_{\Omega}fv.$
2001 ◽
Vol 20
(2)
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pp. 315-330
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2018 ◽
Vol 15
(04)
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pp. 693-719
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1980 ◽
Vol 87
(3)
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pp. 501-513
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2014 ◽
Vol 198
(6)
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pp. 655-676
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1990 ◽
Vol 9
(6)
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pp. 535-544
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