Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global Functional calculus, lower/upper bounds and evolution equations
  on manifolds with boundary   Given a smooth manifold $M$ (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.

1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph