Uniqueness for local-nonlocal elliptic equations

2023/07/05 by Biagi, Stefano, Meglioli, Giulia, Punzo, Fabio
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2307.02209

Abstract

We study mixed local and nonlocal elliptic equation with a variable coefficient ρ. Under suitable assumptions on the behaviour at infinity of ρ, we obtain uniqueness of solutions belonging to certain weighted Lebsgue spaces, with a weight depending on the coefficient ρ. The hypothesis on ρ is optimal; indeed, when it fails we get nonuniqueness of solutions. We also investigate the parabolic counterpart of such equation.

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