Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solvability and optimization for a class of mixed variational problems   We consider an abstract mixed variational problem governed by a nonlinear
operator $A$ and a bifunctional $J$, in a real reflexive Banach space $X$. The
operator $A$ is assumed to be continuous, Lipschitz continuous on each bounded
subset of $X,$ and generalized monotone. First, we pay attention to the unique
solvability of the problem. Next, we prove a continuous dependence result of
the solution with respect to the data. Based on this result we prove the
existence of at least one solution for an associated optimization problem.
Finally, we apply our abstract results to the well-posedness and the
optimization of an antiplane frictional contact model for nonlinearly elastic
materials of Hencky-type.

31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess