Semilinear elliptic equations involving mixed local and nonlocal operators

Stefano Biagi, Eugenio Vecchi, Serena Dipierro, Enrico Valdinoci

Research output: Contribution to journalArticlepeer-review

12 Citations (Web of Science)


In this paper, we consider an elliptic operator obtained as the superposition of a classical second-order differential operator and a nonlocal operator of fractional type. Though the methods that we develop are quite general, for concreteness we focus on the case in which the operator takes the form -Δ + (-Δ)s, with s ∈ (0, 1). We focus here on symmetry properties of the solutions and we prove a radial symmetry result, based on the moving plane method, and a one-dimensional symmetry result, related to a classical conjecture by G.W. Gibbons.

Original languageEnglish
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Publication statusE-pub ahead of print - 14 Oct 2020


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