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

By Anup Biswas and Erwin Topp
We study the existence-uniqueness of solution (u,λ)(u, \lambda) to the ergodic Hamilton-Jacobi equation (-\Delta)^s u + H(x, \nabla u) = f-\lambda\quad \text{in}\; \mathbb{R}^d, and u0u\geq 0, where s(12,1)s\in (\frac{1}{2}, 1). We show that the critical λ=λ\lambda=\lambda^*, defined as the infimum of all λ\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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