We study mixed local and nonlocal elliptic equation with a variable coefficient ρ. Under suitable assumptions on the behavior at infinity of ρ, we obtain uniqueness of solutions belonging to certain weighted Lebesgue 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.
Uniqueness for local-nonlocal elliptic equations
Biagi S.;Meglioli G.;Punzo F.
2025-01-01
Abstract
We study mixed local and nonlocal elliptic equation with a variable coefficient ρ. Under suitable assumptions on the behavior at infinity of ρ, we obtain uniqueness of solutions belonging to certain weighted Lebesgue 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.File in questo prodotto:
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