Work

Uniqueness for local–nonlocal elliptic equations

Year: 2024

Type: article

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

Source: Communications in Contemporary Mathematics

DOI: 10.1142/s0219199725500178

Authors: Stefano Biagi, Giulia Meglioli, Fabio Punzo

Institutions: Politecnico di Milano, Bielefeld University

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Deutsche Forschungsgemeinschaft

Awards: G1288578048, G8147995223, G8201362140, SFB 1283: Unsicherheit beherrschen und Zufall sowie Unordnung nutzen in Analysis, Stochastik und deren Anwendungen