Nonlocal transmission problems with fractional diffusion and boundary conditions on non-smooth interfaces
Ciprian, G. Gal
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We consider a transmission problem consisting of two semilinear parabolic equations involving fractional diffusion operators of different orders in a general non-smooth setting with emphasis on Lipschitz interfaces and transmission conditions along the interface. We give a unified framework for the existence and uniqueness of strong and mild solutions, and their global regularity properties.