The Neumann condition for the superposition of fractional Laplacians

Abstract

We present a new functional setting for Neumann conditions related to the superposition of (possibly infinitely many) fractional Laplace operators. We will introduce some bespoke functional framework and present minimization properties, existence and uniqueness results, asymptotic formulas, spectral analyses, rigidity results, integration by parts formulas, superpositions of fractional perimeters, as well as a study of the associated heat equation.

References in corpus (4)

• A general framework for nonlocal Neumann problems
• An existence theory for superposition operators of mixed order subject to jumping nonlinearities
• An existence theory for nonlinear superposition operators of mixed fractional order
• A general theory for the $(s,p)$-superposition of nonlinear fractional operators

Cited by in corpus (2)

• Some nonlinear problems for the superposition of fractional operators with Neumann boundary conditions
• Logistic diffusion equations governed by the superposition of operators of mixed fractional order