Kramers–Fokker–Planck operators with homogeneous potentials

Autor:	Mona Ben Said
Rok vydání:	2021
Předmět:	Hessian matrix Work (thermodynamics) Polynomial Logarithm General Mathematics Degenerate energy levels General Engineering Mathematics::Spectral Theory symbols.namesake symbols Fokker–Planck equation Laplace operator Eigenvalues and eigenvectors Mathematical physics Mathematics
Zdroj:	Mathematical Methods in the Applied Sciences. 45:914-927
ISSN:	1099-1476 0170-4214
DOI:	10.1002/mma.7822
Popis:	In this article we establish a global subelliptic estimate for Kramers-Fokker-Planck operators with homogeneous potentials $V(q)$ under some conditions, involving in particular the control of the eigenvalues of the Hessian matrix of the potential. Namely, this work presents a different approach from the one in [Ben], in which the case $V (q_1, q _2) =-q ^2_1 (q^ 2_1+q^2_2) ^n$ was already treated only for $n=1.$ With this article, after the former one dealing with non homogeneous polynomial potentials, we conclude the analysis of all the examples of degenerate ellipticity at infinty presented in the framework of Witten Laplacian by Helffer and Nier in [HeNi]. Like in [Ben], our subelliptic lower bounds are the optimal ones up to some logarithmic correction.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::3c8d60ce8a7b77845e05c58602e108c6 https://doi.org/10.1002/mma.7822 Zobrazit plný text záznamu Plný text