A Bourgain-Brezis-Mironescu formula for anisotropic fractional Sobolev spaces and applications to anisotropic fractional differential equations

2022/06/23 by Ignacio Ceresa Dussel, Dussel, Ignacio Ceresa, Julián Fernández Bonder +1
Computer Science · Mathematics · #35J92 #35R11 #46E35 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2206.11873

openalex publication_date 2022/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we prove Bourgain-Brezis-Mironescu's type results (cf. \citeBBM2001) (BBM for short) for an energy functional which is strongly related to the fractional anisotropic p-Laplacian. We also provide with the analogous of Maz'ya-Shaposhnikova (see \citeMS) type results for these energies and finally we apply these results to analyze the stability of solutions to anisotropic fractional p-laplacian equations.

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