Logarithmic Schr\"odinger Equations in Infinite Dimensions
We study the logarithmic Schr\"odinger 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...
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| Format: | Artikel |
| Sprache: | eng |
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| Zusammenfassung: | We study the logarithmic Schr\"odinger 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. |
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| DOI: | 10.48550/arxiv.2203.05374 |