Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimal failure probability for ceramic design via shape control   We consider the probability of failure for components made of brittle mate-
rials under one time application of a load as introduced by Weibull and Batdorf
- Crosse and more recently studied by NASA and the STAU cooperation as an
objective functional in shape optimization and prove the existence of optimal
shapes in the class of shapes with a uniform cone property. The corresponding
integrand of the objective functional has convexity properties that allow to
derive lower-semicontinuity according to Fujii (Opt. Th. Appl. 1988). These
properties require less restrictive regularity assumptions for the boundaries
and state functions compared to [arXiv:1210.4954]. Thereby, the weak
formulation of linear elasticity can be kept for the abstract setting for shape
optimization as presented in the book by Haslinger and Maekinen.

17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ