论文标题
涉及混合本地和非局部运算符的半线性椭圆方程
Semilinear elliptic equations involving mixed local and nonlocal operators
论文作者
论文摘要
在本文中，我们将获得的椭圆操作员视为经典二阶差异操作员和分数类型的非局部操作员的叠加。尽管我们开发的方法非常通用，但对于具体性，我们专注于操作员采用$-δ+（-δ）^s $的情况，并带有$ s \ in（0,1）$。我们在这里关注溶液的对称特性，并基于移动平面方法证明了径向对称性结果，以及与G.W.经典猜想有关的一维对称结果。长臂猿。
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 $s\in(0,1)$. 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.
