论文标题
部分可观测时空混沌系统的无模型预测
Boundedness of Wolff-type potentials and applications to PDEs
论文作者
论文摘要
我们提供了一个简短的证明，证明了Wolff-Havin--Maz'ya的广义版本的急剧重新排列估计。结果，我们证明了该积分运算符的减少原理，即对那些重新排列的不变空间的表征，在该空间之间，电势通过Hardy类型的一维不平等界定。由于已知所述潜力的特殊情况可以控制非标准生长的一系列质椭圆形PDE的较弱的解决方案，因此我们推断出在规定的数据类别中重新安排不变空间中解决方案的局部规则性能。
We provide a short proof of a sharp rearrangement estimate for a generalized version of a potential of Wolff--Havin--Maz'ya type. As a consequence, we prove a reduction principle for that integral operators, that is, a characterization of those rearrangement invariant spaces between which the potentials are bounded via a one-dimensional inequality of Hardy-type. Since the special case of the mentioned potential is known to control precisely very weak solutions to a broad class of quasilinear elliptic PDEs of non-standard growth, we infer the local regularity properties of the solutions in rearrangement invariant spaces for prescribed classes of data.
