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arXiv · 2307.02209

Uniqueness for local-nonlocal elliptic equations

Stefano Biagi·Giulia Meglioli·Fabio Punzo
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Abstract

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

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Stefano Biagi, Giulia Meglioli, Fabio Punzo. 2023-07-05. Uniqueness for local-nonlocal elliptic equations. https://arxiv.org/abs/2307.02209

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