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.

Biagi, S., Vecchi, E., Dipierro, S., Valdinoci, E. (2021). Semilinear elliptic equations involving mixed local and nonlocal operators. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS, 151(5), 1611-1641 [10.1017/prm.2020.75].

Semilinear elliptic equations involving mixed local and nonlocal operators

Vecchi, Eugenio;
2021

Abstract

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.
2021
Biagi, S., Vecchi, E., Dipierro, S., Valdinoci, E. (2021). Semilinear elliptic equations involving mixed local and nonlocal operators. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS, 151(5), 1611-1641 [10.1017/prm.2020.75].
Biagi, Stefano; Vecchi, Eugenio; Dipierro, Serena; Valdinoci, Enrico
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/831665
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