Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A regularized penalty-multiplier method for approximating cavitation
  solutions with prescribed cavity volume size   Let $\Omega\in\mathbb{R}^n$ be the region occupied by a body and let
$\mathbf{x}_0$ be a flaw point in $\Omega$. Let $E(\cdot)$ be an energy
functional (defined on some appropriate admissible set of deformations of
$\Omega$). For $V>0$ fixed, we let $\mathbf{u}_V$ be a minimizer of $E(\cdot)$
among the set of deformations constrained to form a hole of volume $V$ at
$\mathbf{x}_0$. In this paper we describe a regularized penalty--multiplier
method and its convergence properties for the computation of both
$\mathbf{u}_V$ and $E(\mathbf{u}_V)$. In particular, we show that as the
regularization parameter goes to zero, the regularized constrained minimizers
converge weakly in
$W^{1,p}(\Omega\setminus\overline{\mathcal{B}_{\delta}(\mathbf{x}_0)})$ to
$\mathbf{u}_{V}$ for any $\delta>0$. We describe as well the main features of a
numerical scheme for approximating $\mathbf{u}_V$ and $E(\mathbf{u}_V)$ and
give a numerical example for the case of a stored energy for an elastic fluid.

37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci