Salvato in:
| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2602.21665 |
| Tags: |
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Sommario:
- We give a certain $L^{\infty}(\mathbb{R}^2)$-estimate for the heat semigroup $\{e^{tΔ}\}_{t \ge 0}$ that is closely related to the fact $H^1(\mathbb{R}^2) \not\subset L^{\infty}(\mathbb{R}^2)$, i.e., the critical Sobolev (non-)embedding and the standard Brezis-Gallouët inequality. While we provide several approaches to show such an assertion, we also reveal that the time-singularity of our estimate as $t \to 0^+$ is indeed optimal.