9 problems

Affine adjoint ansatz. We conjecture that

Strong Laplace Hopf-lemma conjecture. If, in addition, $u_t(0,0)=0$, then

Hopf-type curvature comparison problem. Is it true that either $u\equiv v$ near $(0,0)$ or $v\equiv0$ near $(0,0)$? The source describes this as a plausible variation of the Hopf L…

Generalization conjecture. Such multi-dimensional linear SDVIEs should be treatable by the same maximum-principle method described above.

Effective maximum-principle conjecture. Then

Consider a control-affine system with controls taking values in an unbounded set, and its associated extended, impulsive system. Assume that an optimal process exists for the non-i…

Maximum principle conjecture. There is a constant $C=C(d,s)$ such that

A vanishing function is a function whose constant terms $C_v(a,b)$ in maximum-principle-function condition (IV) vanish for all $0<a,b$. A maximum-principle function (MPF) is a func…

Let $H$ be the underlying Hilbert space, let $T>0$, and let $K$ be an operator-valued progressively measurable process. Theorem 10.1 establishes a conclusion for a more restricted…