一类非标准增长泛函极小的某些性质

Certain properties of Minimizers of a Functional with Nonstandard Growth Conditions

设ε〉０，ｋ≥１，ｆ（ｔ）＝（ε＋ｔ）＾ｋｌｎ（１＋ｔ），在Ｅ＾ｎ中的有界区域Ｇ上考虑向量值函数ｕ的泛函：Ｉ（ｕ）＝∫ｇｆ（│△↓ｕ│＾２）ｄｘ，本文研讨了泛函极小的某些性质。

Abstract: Consider on G,a bounded domain in En .the following functional:of which u is a vector valued function and f(t ) = (ε+t )kln (1+t),ε>0, k≥1.Certain properties of the minimizer of I (u)are discussed .that is, v( ) is bounded locally in G and the higher integrability of is proved. Where ds and.