Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Estimates for solutions of Dirac equations and an application to a
  geometric elliptic-parabolic problem   We develop estimates for the solutions and derive existence and uniqueness
results of various local boundary value problems for Dirac equations that
improve all relevant results known in the literature. With these estimates at
hand, we derive a general existence, uniqueness and regularity theorem for
solutions of Dirac equations with such boundary conditions. We also apply these
estimates to a new nonlinear elliptic-parabolic problem, the Dirac-harmonic
heat flow on Riemannian spin manifolds. This problem is motivated by the
supersymmetric nonlinear $\sigma$-model and combines a harmonic heat flow type
equation with a Dirac equation that depends nonlinearly on the flow.

17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas