Logarithmic Schr\"odinger Equations in Infinite Dimensions
Abstract
We study the logarithmic Schr\"odinger equation with finite range potential on RZd. 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.
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