Global Functional calculus, lower/upper bounds and evolution equations on manifolds with boundary
Analysis of PDEs
2021-01-08 v1 Differential Geometry
Functional Analysis
Abstract
Given a smooth manifold (with or without boundary), in this paper we establish a global functional calculus (without the standard assumption that the operators are classical pseudo-differential operators) and the G\r{a}rding inequality for global pseudo-differential operators associated with boundary value problems. The analysis that we follow is free of local coordinate systems. Applications of the G\r{a}rding inequality to the global solvability for a class of evolution problems are also considered.
Cite
@article{arxiv.2101.02519,
title = {Global Functional calculus, lower/upper bounds and evolution equations on manifolds with boundary},
author = {Duván Cardona and Vishvesh Kumar and Michael Ruzhansky and Niyaz Tokmagambetov},
journal= {arXiv preprint arXiv:2101.02519},
year = {2021}
}
Comments
35 pages. arXiv admin note: text overlap with arXiv:1504.00777