Acta mathematica scientia, Series B >
THE REGULARITY OF QUASI-MINIMA AND ω-MINIMA OF INTEGRAL FUNCTIONALS
Received date: 2008-01-15
Revised date: 2008-05-20
Online published: 2010-07-20
Supported by
Supported by the Program of Fujian Province-Hong Kong
In this article, we have two parts. In the first part, we are concerned with the locally Holder continuity of quasi-minima of the following integral functional
∫Ω f(x, u, Du) dx, (1)
where Ω is an open subset of Euclidean N-space (N ≥3), u: Ω→R, the Carath\'eodory function f satisfies the critical Sobolev exponent growth condition
|Du|p-|u|p*-a(x)l≤ f(x, u, Du)≤ L(|Du|p+|u|p*+a(x)), (2)
where L≤1, 1<p<N, p*=Np/N-p, and a(x) is a nonnegative function that lies in a suitable Lp space. In the second part, we study the locally H\"{o}lder continuity of ω-minima of (1). Our method is to compare the ω-minima of (1) with the minima of corresponding function determined by its critical Sobolev exponent growth condition. Finally, we obtain the regularity by Ekeland's variational principal.
NING Zheng-Yuan , WANG Xiu-Li . THE REGULARITY OF QUASI-MINIMA AND ω-MINIMA OF INTEGRAL FUNCTIONALS[J]. Acta mathematica scientia, Series B, 2010 , 30(4) : 1301 -1317 . DOI: 10.1016/S0252-9602(10)60126-9
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