论文标题
抛物线薄障碍问题的几乎最小化器的规律性
Regularity of almost minimizers for the parabolic thin obstacle problem
论文作者
论文摘要
在本文中，我们研究了几乎最小化的抛物线稀薄障碍物（或Signorini）问题，这些问题与零障碍物有关。我们建立了他们的$ h^{σ，σ/2} $ - 每$ 0 <σ<1 $，以及$ h^{β{β，β/2} $ - 在薄薄空间的任一侧的空间梯度的规律性，对于约$ 0 <β<1 $。对于可变的Hölder系数的Signorini问题，几乎最小化也获得了类似的结果。
In this paper, we study almost minimizers for the parabolic thin obstacle (or Signorini) problem with zero obstacle. We establish their $H^{σ,σ/2}$-regularity for every $0<σ<1$, as well as $H^{β,β/2}$-regularity of their spatial gradients on the either side of the thin space for some $0<β<1$. A similar result is also obtained for almost minimizers for the Signorini problem with variable Hölder coefficients.
