论文标题
关于最小化非本地能量的一般形式的度量的存在和界限
On the existence and boundedness of minimizing measures for a general form of non-local energies
论文作者
论文摘要
在本文中，我们考虑了积分形式的非本地能量的一种非常通用的形式，该形式涵盖了大多数通常的能量（例如，正和负能量的总和）。我们不接受仅作为可接受的对象的集合或$ l^\ infty $函数，而是为所有ra措施定义了能量。我们证明了在广泛的一般性中存在最佳度量的存在，并且我们表明，在某些情况下，最佳度量实际上是$ l^\ infty $函数，提供了对其规范的先验限制。我们还获得了最小化器的独特结果。
In this paper we consider a very general form of a non-local energy in integral form, which covers most of the usual ones (for instance, the sum of a positive and a negative power). Instead of admitting only sets, or $L^\infty$ functions, as admissible objects, we define the energy for all the Radon measures. We prove the existence of optimal measures in a wide generality, and we show that in several cases the optimal measures are actually $L^\infty$ functions, providing an a priori bound on their norm. We also derive a uniqueness result for minimizers.
