Viscosity Solutions for a System of Integro-PDEs and Connections to Optimal Switching and Control of Jump-Diffusion Processes

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Linear theory for a mixed operator with Neumann conditions (2020, unknown): “In terms of theory and applications, we recall that operators with mixed classical and fractional orders have been studied under different points of views, see for instance [1,2,4,6–10,12,13,18,19,21,25–27, 31–33,40,47,48] and the references therein.”
Regularity results for solutions of mixed local and nonlocal elliptic equations (2022, background): “Moreover, mixed operators have recently received a great attention from different points of view, including regularity theory [2, 3, 8, 10, 12, 14, 15, 17, 25], existence and non-existence results [1, 6, 28], eigenvalue problems [13, 16, 22], shape optimization and calculus of variations [7, 11], sy”
A Brezis-Nirenberg type result for mixed local and nonlocal operators (2022, unknown): “The contemporary investigation has speciﬁcally focused on several problems in the existence and regularity theory (see [1,4,5, 8,11,12,16–18,22 The stirring motivation for the problems presented in this paper comes from the study of nonlinear problems with critical exponents, as the ones suggested…”