湖南师范大学自然科学学报
湖南師範大學自然科學學報
호남사범대학자연과학학보
ACTA SCIENTIARUM NATURALIUM UNIVERSITATIS NORMALIS HUNANENSIS
2014年
4期
72-76,95
,共6页
非齐次A-调和方程%双障碍问题%优化控制%Hodge分解%W1,q (Ω)-正则性
非齊次A-調和方程%雙障礙問題%優化控製%Hodge分解%W1,q (Ω)-正則性
비제차A-조화방정%쌍장애문제%우화공제%Hodge분해%W1,q (Ω)-정칙성
non-homogeneous A-harmonic equation%double obstacle problems%optimal control%Hodge de-composition%W1,q-regularity
应用Hodge分解定理,得到了非齐次A-调和方程-divA(x,Du(x))=f(x,u(x))对应控制的双障碍问题的很弱解W1,q(Ω)-正则性,其中,A(x,Du(x)),f(x,u(x))满足文中所给的条件,从而推广了相关文献中的有关结果。该结果在优化控制问题中有着广泛的应用。
應用Hodge分解定理,得到瞭非齊次A-調和方程-divA(x,Du(x))=f(x,u(x))對應控製的雙障礙問題的很弱解W1,q(Ω)-正則性,其中,A(x,Du(x)),f(x,u(x))滿足文中所給的條件,從而推廣瞭相關文獻中的有關結果。該結果在優化控製問題中有著廣汎的應用。
응용Hodge분해정리,득도료비제차A-조화방정-divA(x,Du(x))=f(x,u(x))대응공제적쌍장애문제적흔약해W1,q(Ω)-정칙성,기중,A(x,Du(x)),f(x,u(x))만족문중소급적조건,종이추엄료상관문헌중적유관결과。해결과재우화공제문제중유착엄범적응용。
Using Hodge decomposition theorem , W1,q (Ω) -regularity for very weak solutions to double obsta-cle problems associated with non-homogeneous A-harmonic equations div(A(x,Du(x)))=f(x,u(x)) is obtained under certain conditions on A( x,Du( x) ) ,f( x,u( x) ) listed in the context , and therefore the corresponding results in related literatures are generalized .The results could be widely used in optimal control problems .