Existence of bounded solutions of fully nonlinear elliptic equations modeling the first passage time in cylindrical domains
Antonio Di Crescenzo, Serena Spina, Antonio Vitolo · Differential and Integral Equations · 2023
The aim of this paper is to establish existence and uniqueness of bounded viscosity solutions of fully nonlinear second-order elliptic equations in domains like slabs and cylinders. A global Hölder regularity is also proved. The issue is motivated by different applications based on the First Passage Time (FPT). In particular, the equations modelize the expected value of the FPT for a time-homogeneous stochastic process. Explicit solutions have been computed for the Wiener process, and the influence of a drift term on the mean first hitting time has been also discussed.