Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heat trace asymptotics and compactness of isospectral potentials for the
  Dirichlet Laplacian   Let $\Omega$ be a $C^\infty$-smooth bounded domain of $\mathbb{R}^n$, $n \geq
1$, and let the matrix ${\bf a} \in C^\infty (\overline{\Omega};\R^{n^2})$ be
symmetric and uniformly elliptic. We consider the $L^2(\Omega)$-realization $A$
of the operator $-\mydiv ( {\bf a} \nabla \cdot)$ with Dirichlet boundary
conditions. We perturb $A$ by some real valued potential $V \in C_0^\infty
(\Omega)$ and note $A_V=A+V$. We compute the asymptotic expansion of
$\mbox{tr}\left( e^{-t A_V}-e^{-t A}\right)$ as $t \downarrow 0$ for any matrix
${\bf a}$ whose coefficients are homogeneous of degree $0$. In the particular
case where $A$ is the Dirichlet Laplacian in $\Omega$, that is when ${\bf a}$
is the identity of $\R^{n^2}$, we make the four main terms appearing in the
asymptotic expansion formula explicit and prove that $L^\infty$-bounded sets of
isospectral potentials of $A$ are $H^s$-compact for $s <2$.

4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio