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arXiv · 2306.09795

Parabolic $α$-Riesz flows and limit cases $α\to 0^+$, $α\to d^-$

Lucia De Luca·Massimiliano Morini·Marcello Ponsiglione·Emanuele Spadaro
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Abstract

In this paper we introduce the notion of parabolic $α$-Riesz flow, for $α\in(0,d)$, extending the notion of $s$-fractional heat flows to negative values of the parameter $s=-\fracα{2}$. Then, we determine the limit behaviour of these gradient flows as $α\to 0^+$ and $α\to d^-$. To this end we provide a preliminary $Γ$-convergence expansion for the Riesz interaction energy functionals. Then we apply abstract stability results for uniformly $λ$-convex functionals which guarantee that $Γ$-convergence commutes with the gradient flow structure.

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Lucia De Luca, Massimiliano Morini, Marcello Ponsiglione, Emanuele Spadaro. 2023-06-16. Parabolic $α$-Riesz flows and limit cases $α\to 0^+$, $α\to d^-$. https://arxiv.org/abs/2306.09795

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