L. De Luca - M. Morini - M. Ponsiglione - E. Spadaro
Parabolic $\alpha$-Riesz flows and limit cases $\alpha\to 0^+$, $\alpha\to d^-$
Preprint
Inserted: 16 jun 2023
Last Updated: 16 jun 2023
Year: 2023
Abstract:
In this paper we introduce the notion of parabolic $\alpha$-Riesz flow, for $\alpha\in(0,d)$, extending the notion of $s$-fractional heat flows to negative values of the parameter $s=-\frac{\alpha}{2}$. Then, we determine the limit behaviour of these gradient flows as $\alpha \to 0^+$ and $\alpha \to d^-$.
To this end we provide a preliminary $\Gamma$-convergence expansion for the Riesz interaction energy functionals. Then we apply abstract stability results for uniformly $\lambda$-convex functionals which guarantee that $\Gamma$-convergence commutes with the gradient flow structure.
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