Preface

Autor: Nicola Abatangelo, Eugenio Vecchi

Publikováno v: Bruno Pini Mathematical Analysis Seminar, Vol 14, Iss 1, Pp i-iv (2023)

Nonlinear PDEs is one of the traditional topics developed by the Italian school of Analysis since its early days. These have recently met with the theory of nonlocal operators, which has been a trending topic in the international community in the pas

Externí odkaz: https://doaj.org/article/3e8495111e3f4e00adac5e86de88966e

Fractional Laplacians on ellipsoids

Autor: Nicola Abatangelo, Sven Jarohs, Alberto Saldaña

Publikováno v: Mathematics in Engineering, Vol 3, Iss 5, Pp 1-34 (2021)

We show explicit formulas for the evaluation of (possibly higher-order) fractional Laplacians~$\Ds$ of some functions supported on ellipsoids. In particular, we derive the explicit expression of the torsion function and give examples of~$s$-harmonic

Externí odkaz: https://doaj.org/article/79f12c018e2843b3ab078b3f68d339be

Fractional Laplacians on ellipsoids

Autor: Alberto Saldaña, Sven Jarohs, Nicola Abatangelo

Publikováno v: Mathematics in Engineering, Vol 3, Iss 5, Pp 1-34 (2021)

We show explicit formulas for the evaluation of (possibly higher-order) fractional Laplacians of some functions supported on ellipsoids. In particular, we derive the explicit expression of the torsion function and give examples of $s$-harmonic functi

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::11d09ae6951432cd1a46b3b661e8ce8b
http://arxiv.org/abs/2005.09514

A remark on nonlocal Neumann conditions for the fractional Laplacian

Autor: Nicola Abatangelo

We show how nonlocal boundary conditions of Robin type can be encoded in the pointwise expression of the fractional operator. Notably, the fractional Laplacian of functions satisfying homogeneous nonlocal Neumann conditions can be expressed as a regi

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e67f80e40dd78b82c56aedcf1f2cb49a
http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/63790

Nonhomogeneous boundary conditions for the spectral fractional Laplacian

Autor: Nicola Abatangelo, Louis Dupaigne

Publikováno v: Annales de l'Institut Henri Poincaré (C) Non Linear Analysis
Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2016, ⟨10.1016/j.anihpc.2016.02.001⟩

We present a construction of harmonic functions on bounded domains for the spectral fractional Laplacian operator and we classify them in terms of their divergent profile at the boundary. This is used to establish and solve boundary value problems as

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::83bc53dfdba4836d927ee8a1ed903173
https://doi.org/10.1016/j.anihpc.2016.02.001