By Anup Biswas and Erwin Topp

We study the existence-uniqueness of solution $(u, \lambda)$ to the ergodic Hamilton-Jacobi equation $$(-\Delta)^s u + H(x, \nabla u) = f-\lambda\quad \text{in}\; \mathbb{R}^d,$$ and $u\geq 0$, where $s\in (\frac{1}{2}, 1)$. We show that the critical $\lambda=\lambda^*$, defined as the infimum of all $\lambda$ attaining a non-negative supersolution, attains a nonnegative... Show more

October 21, 2023

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Nonlocal ergodic control problem in $\mathbb{R}^d$

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