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Explicit improvements for $\mathrm{L}^p$-estimates related to elliptic systems
- Publication Year :
- 2023
-
Abstract
- We give a simple argument to obtain $\mathrm{L}^p$-boundedness for heat semigroups associated to uniformly strongly elliptic systems on $\mathbb{R}^d$ by using Stein interpolation between Gaussian estimates and hypercontractivity. Our results give $p$ explicitly in terms of ellipticity. It is optimal at the endpoint $p=\infty$. We also obtain $\mathrm{L}^p$-estimates for the gradient of the semigroup, where $p>2$ depends on ellipticity but not on dimension.<br />Comment: 16 pages, improved readability, accepted for publication in Bulletin of the LMS
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2302.09039
- Document Type :
- Working Paper