In [4], the authors proved the uniqueness among the solutions which admit every exponential moments. In this paper, we prove that uniqueness holds among solutions which admit some given exponential moments. These exponential moments are natural as they are given by the existence theorem. Thanks to this uniqueness result we can strengthen the nonlinear Feynman-Kac formula proved in [4].

In recent work, Simsek-Ozdaglar-Acemoglu [5] prove a generalization of the Poincare-Hopf Theorem and establish sufficient conditions for the uniqueness of generalized critical points (generalized equilibria) under some regularity assumptions. In this paper, we restrict ourselves to functions on box-constrained regions and establish the uniqueness of the generalized critical point with weaker re...

We derive a global index theorem for degenerate variational inequality problems defined by a continuously differentiable function F over a convex set M represented by a finite number of inequality constraints. Our index theorem can be applied when the solutions are non-singular and possibly degenerate, as long as they also satisfy the injective normal map property, which is implied by strong st...

Abstract We consider analytically weak solutions to semilinear stochastic partial differential equations with non-anticipating coefficients driven by a cylindrical Brownian motion. The are allowed take values in Banach spaces. show that uniqueness is equivalent joint uniqueness, and thereby generalize theorem A.S. Cherny an infinite dimensional setting. Our proof for the technical key step diff...

Shannon entropy [1] is one of fundamental quantities in classical information theory and uniquely determinded by the Shannon-Khinchin axiom or the Faddeev axiom. One-parameter extensions for Shannon entropy have been studied by many researchers. The Rényi entropy [2] and the Tsallis entropy [3] are famous. In the paper [4], the uniqueness theorem for the Tsallis entropy was proved. Also, in our...

Of course, the answer to the question posed in the title is no, in general, but, surprisingly enough, yes in a significant situation to be detailed later. This paper aims to bring to the attention of the widest possible mathematical audience an elementary result, based on the theorem of differentiation of inverse functions, which extends the applicability of uniqueness theorems. Loosely speakin...

I review the black hole uniqueness theorem and the no hair theorems established for physical black hole stationary states by the early 80’. This review presents the original and decisive work of Carter, Robinson, Mazur and Bunting on the problem of no bifurcation and uniqueness of physical black holes. Its original version was written only few years after my proof of the Kerr-Newman et al. blac...