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arXiv · 1511.02893

Extension Properties and Boundary Estimates for a Fractional Heat Operator

K. Nyström·O. Sande
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Abstract

The square root of the heat operator $\sqrt{\partial_t-Δ}$, can be realized as the Dirichlet to Neumann map of the heat extension of data on $\mathbb R^{n+1}$ to $\mathbb R^{n+2}_+$. In this note we obtain similar characterizations for general fractional powers of the heat operator, $(\partial_t-Δ)^s$, $s\in (0,1)$. 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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K. Nyström, O. Sande. 2015-11-09. Extension Properties and Boundary Estimates for a Fractional Heat Operator. https://arxiv.org/abs/1511.02893

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