Sentence examples for moving plane method from inspiring English sources

The standard tool to obtain the radial symmetry for a system of equations is the moving plane method (MPM).

In this section, we use the moving plane method to prove Theorem 1.1.

The monotonicity of (u_{0}) is shown via the moving plane method.

The main technique is a generalization of the moving plane method to the Heisenberg group.

Applying the H-reflection and the moving plane method, we prove that the cylindrical solution of (1.1) is monotone.

end{aligned}We now use the moving plane method to prove the symmetry property of v, which is defined on a ball.

Firstly, using the moving planes method in integral forms, we have the following symmetric result.

In Section 2, we show that ( u, v, w ) is radially symmetric by the moving planes method.

In particular, it was considered in [2, 4] the radial symmetry and monotonicity of nonnegative solutions of nonlinear elliptic equations by the moving planes method.

We show that every positive solution triple ( u, v, w ) of the system is radially symmetric and monotonic decreasing about some point by the moving planes method in integral forms.

The symmetry of the solutions to nonlinear elliptic problems are in general investigated by the moving planes method, which was first used by Alexanderoff for differential equations, and developed by Serrin [1], Gidas et al. [2], Caffarelli et al. [3] etc.