Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonlinear semigroups generated by $j$-elliptic functionals   We generalise the theory of energy functionals used in the study of gradient
systems to the case where the domain of definition of the functional cannot be
embedded into the Hilbert space $H$ on which the associated operator acts, such
as when $H$ is a trace space. We show that under weak conditions on the
functional $\varphi$ and the map $j$ from the effective domain of $\varphi$ to
$H$, which in opposition to the classical theory does not have to be injective
or even continuous, the operator on $H$ naturally associated with the pair
$(\varphi ,j)$ nevertheless generates a nonlinear semigroup of contractions on
$H$. We show that this operator, which we call the $j$-subgradient of
$\varphi$, is the (classical) subgradient of another functional on $H$, and
give an extensive characterisation of this functional in terms of $\varphi$ and
$j$. In the case where $H$ is an $L^2$-space, we also characterise the
positivity, $L^\infty$-contractivity and existence of order-preserving
extrapolations to $L^q$ of the semigroup in terms of $\varphi$ and $j$. This
theory is illustrated through numerous examples, including the
$p$-Dirichlet-to-Neumann operator, general Robin-type parabolic boundary value
problems for the $p$-Laplacian on very rough domains, and certain coupled
parabolic-elliptic systems.

18
The categories of this paper are: econ
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th