Extension properties and boundary estimates for a fractional heat operator

By Kaj Nyström, Olow Sande. 2015

63 citations recorded by the source corpus.

The square root of the heat operator $\sqrt{\partial_t-\Delta}$, 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 n ...

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/457c4a85029bea2bd93a3b3f4e3a4dc7934055b1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

On the regularity of the non-dynamic parabolic fractional obstacle problem (2016, background): “By the Lγ(:= div(y γ∇)− y∂t)-caloric extension formula (see [22] and [21]) in all of R (3.”
The Mathematical Theories of Diffusion: Nonlinear and Fractional Diffusion (2017, methodology): “• A different approach is taken by Nyström-Sande [201] and Stinga-Torrea [231], who define the fractional powers of the whole heat operator and solve (2.15) (∂t −∆)su(t, x) = f(t, x), for 0 s 1.”
Monotonicity of generalized frequencies and the strong unique continuation property for fractional parabolic equations (2017, methodology): “ nonlocal operators, and similarly to what was done in [FF] and [Ru1] in the stationary case, 8 MONOTONICITY OF GENERALIZED FREQUENCIES, ETC. our approach consists in using the extension procedure in [NS], [ST] and thus work with a local operator. However, as we have already mentioned in Section 1, ”