14 problems

Let $X$ be a Banach space, and let $A$ and $B$ be multi-valued maximal monotone operators on $X$. Rockafellar's maximal monotonicity of the sum conjecture. If … then the sum $A+B$…

Positive-corotational-rate conjecture. The equivalence is conjectured to hold for every such rate:

Corotational stability for the Green–Naghdi rate. The following equivalence is conjectured:

Corotational stability characterization. This characterization is conjectured to hold for a large class of reasonable corotational rates: the stability condition is equivalent to s…

Let $\mathcal{E}: \operatorname{Sym}^{++}(3) \to \operatorname{Sym}(3)$ be a spatial strain tensor with strongly monotone scale function $e: \mathbb{R}^+ \to \mathbb{R}$. For a cor…

Let $V\to H\to V^*$ be the compact Gelfand triple from the assumptions, let $A$ satisfy the stated local monotonicity and coercivity hypotheses, and let…

A maximally monotone structure is a structure with the maximal-monotonicity property in the port-Hamiltonian framework. A Dirac structure represents a power-conserving interconnect…

Let $E$ be the Banach space in the paper, let $S$ be a quasidense operator, and let $\varphi_S$ and $\theta_S$ be the associated functions on $E\times E^*$ and $E^*\times E^{**}$,…

Let $X$ be a one-dimensional or higher-dimensional setting with a vector $e$ and an operator $A_e$ whose degree of cyclic monotonicity is being considered. The endpoint cases are t…

Limiting coderivative characterization. $T$ is locally strongly maximally monotone around $(\bar{x},\bar{v})$ if and only if $T$ is hypomonotone around $(\bar{x},\bar{v})$ and…

Let $X$ be a nonreflexive real Banach space. A Banach space is of type (D) if every maximal monotone operator on it is of type (D), where a maximal monotone operator…

Previous examples of non-type (D) maximal monotone operators occurred only on spaces such as $\ell^1$, $L^1$, and Banach spaces containing isometric copies of these spaces. This mo…

Let $F\colon\mathbb{R}^n\rightrightarrows\mathbb{R}^n$ be a maximal monotone mapping. Then the maximal monotone mapping relative-boundary image conjecture. The image of the map…

Let $X$ be a Banach space and let $A$ be a continuous linear monotone operator on $X$. An autoconjugate representer of $A$ is a function representing $A$ that coincides with its co…