| Autor: |
De Luca, Lucia, Morini, Massimiliano, Ponsiglione, Marcello, Spadaro, Emanuele |
| Rok vydání: |
2023 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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