Homogenization of Nonlinear Unilateral Problems
Homogenization of Nonlinear Unilateral Problems
复制标题
非线性单边问题的均质化
DOI：
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发表时间：
1991
期刊：
影响因子：
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通讯作者：
F. Murat
中科院分区：
文献类型：
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作者：
L. Boccardo;F. Murat
In this paper we consider the unilateral problems
$$ left{ egin{gathered} {u_{varepsilon }} in Kleft( {{psi_{varepsilon }}}
ight) hfill \ leftlangle {{A_{varepsilon }}left( {{u_{varepsilon }}}
ight) - f,v - {u_{varepsilon }}}
ight
angle geqslant 0 hfill \ forall v in Kleft( {{psi_{varepsilon }}}
ight) hfill \ end{gathered}
ight. $$
(*)
where the right hand side f is fixed in W−1,P’(Ω) and where the Ae(v) are monotone operators acting from (Inline 1) into W−1,p’(Ω) defined by
$$ {A_{varepsilon }}(v) = - divleft( {{a_{varepsilon }}left( {x,Dv}
ight)}
ight);, $$
while the unilateral convex sets K(ψe) are defined by
$$ Kleft( {{psi_{varepsilon }}}
ight) = left{ {v in W_0^{{1,p}}left( Omega
ight):v geqslant {psi_{varepsilon }};a.e.;in;Omega }
ight};. $$
In this paper we consider the unilateral problems
$$ left{ egin{gathered} {u_{varepsilon }} in Kleft( {{psi_{varepsilon }}}
ight) hfill \ leftlangle {{A_{varepsilon }}left( {{u_{varepsilon }}}
ight) - f,v - {u_{varepsilon }}}
ight
angle geqslant 0 hfill \ forall v in Kleft( {{psi_{varepsilon }}}
ight) hfill \ end{gathered}
ight. $$
(*)
where the right hand side f is fixed in W−1,P’(Ω) and where the Ae(v) are monotone operators acting from (Inline 1) into W−1,p’(Ω) defined by
$$ {A_{varepsilon }}(v) = - divleft( {{a_{varepsilon }}left( {x,Dv}
ight)}
ight);, $$
while the unilateral convex sets K(ψe) are defined by
$$ Kleft( {{psi_{varepsilon }}}
ight) = left{ {v in W_0^{{1,p}}left( Omega
ight):v geqslant {psi_{varepsilon }};a.e.;in;Omega }
ight};. $$