Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Regularity and energy of second order hyperbolic boundary value problems
  on non-timelike hypersurfaces   We study the second order hyperbolic equations with initial conditions, a
nonhomogeneous Dirichlet boundary condition and a source term. We prove the
solution possesses $H^1$ regularity on any piecewise $C^1$-smooth non-timelike
hypersurfaces. We generalize the notion of energy to these hypersurfaces, and
establish an estimate of the difference between the energies on the
hypersurface and on the initial plane where the time $t = 0$. The energy is
shown to be conserved when the source term and the boundary datum are both
zero. We also obtain an $L^2$ estimate for the normal derivative of the
solution. In the proofs we first show these results for $C^2$-smooth solutions
by using the multiplier methods, and then we go back to the original results by
approximation.

34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph