Back to Search
Start Over
Gradient estimates for fundamental solutions of a Schrodinger operator on stratified Lie groups.
- Source :
- Proceedings of the American Mathematical Society; May2024, Vol. 152 Issue 5, p2069-2085, 17p
- Publication Year :
- 2024
-
Abstract
- Let \mathcal L=-\Delta _{\mathbb {G}}+\Upsilon be a Schrödinger operator with a nonnegative potential \Upsilon belonging to the reverse Hölder class B_{Q/2}, where Q is the homogeneous dimension of the stratified Lie group \mathbb {G}. Inspired by Shen's pioneer work and Li's work, we study fundamental solutions of the Schrödinger operator \mathcal L on the stratified Lie group \mathbb {G} in this paper. By proving an exponential decreasing variant of mean value inequality, we obtain the exponential decreasing upper estimates, the local Hölder estimates and the gradient estimates of the fundamental solutions of the Schrödinger operator \mathcal L on the stratified Lie group. As two applications, we obtain the De Giorgi-Nash-Moser theory on the improved Hölder estimate for the weak solutions of the Schrödinger equation and a Liouville-type lemma for \mathcal {L}-harmonic functions on \mathbb {G}. [ABSTRACT FROM AUTHOR]
- Subjects :
- SCHRODINGER operator
SCHRODINGER equation
LIE groups
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 152
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 176473193
- Full Text :
- https://doi.org/10.1090/proc/16684