Extension properties and boundary estimates for a fractional heat operator. (July 2016) - Nyström, K.; Sande, O.
Abstract: The square root of the heat operator ∂ t − Δ, can be realized as the Dirichlet to Neumann map of the heat extension of data on R n + 1 to R + n + 2 . In this note we obtain similar characterizations for general fractional powers of the heat operator, ( ∂ t − Δ ) s, s ∈ ( 0, 1 ) . Using the characterizations we derive properties and boundary estimates for parabolic integro-differential equations from purely local arguments in the extension problem.