论文标题
无限维度中的对数Schrödinger方程
Logarithmic Schrödinger Equations in Infinite Dimensions
论文作者
论文摘要
我们在$ \ Mathbb {r}^{\ Mathbb {z}^d} $上研究具有有限范围潜力的对数Schrödinger方程。通过地面代表，我们将全球吉布斯衡量并表明它满足对数Sobolev的不平等。我们发现在任意维度中的解决方案的估计值，并证明了无限维库奇问题的弱解决方案的存在。
We study the logarithmic Schrödinger equation with finite range potential on $\mathbb{R}^{\mathbb{Z}^d}$. Through a ground-state representation, we associate and construct a global Gibbs measure and show that it satisfies a logarithmic Sobolev inequality. We find estimates on the solutions in arbitrary dimension and prove the existence of weak solutions to the infinite-dimensional Cauchy problem.
