H(o)rmander向量场型积分泛函的极小元的可积性和有界性
Journal of Mathematics（2021）
Abstract
本文考虑H(o)rmander向量场型积分泛函,当边界值具有更高可积性时,借助H(o)rmander向量场上的Sobolev不等式和Stampacchia的迭代公式证明此积分泛函的极小元也会有更高可积性.此外还得到极小元的L1(Ω)和L∞(Ω)有界性,从而把Leonetti和Siepe[12]以及Leonetti和Petricca[13]的结果从欧式空间延拓到H(o)rmander向量场.
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Key words
H(o)rmander's vector fields,Integral functional,Minimizers,Integrability,Boundedness
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