摘要
In this paper the regularity of the Lagrangians f（x,ζ）=|ζ|<sup>α（x）</sup> （1【α<sub>1</sub> α（x） α<sub>2</sub>【 +∞） is studied. Our main result: If α（x） is Holder continuous, then the Lagrangian f（x,ζ）=|ζ|<sup>α（x）</sup> is regular. This result gives a negative answer to a conjecture of V. Zhikov.
In this paper the regularity of the Lagrangians f（x,ζ）=|ζ|<sup>α（x）</sup> （1<α<sub>1</sub> α（x） α<sub>2</sub>< +∞） is studied. Our main result: If α（x） is Holder continuous, then the Lagrangian f（x,ζ）=|ζ|<sup>α（x）</sup> is regular. This result gives a negative answer to a conjecture of V. Zhikov.
基金
Supported by the National Natural Science Foundation of China.
