Extension Properties and Boundary Estimates for a Fractional Heat Operator

2015/11/09 by Nyström, K., Sande, O. · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1511.02893

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 \mathbb Rⁿ⁺¹ to \mathbb Rⁿ⁺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.

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• A monotonicity formula for a semilinear fractional parabolic equation
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