Asymptotic symmetry of solutions of nonlinear partial differential equations

Abstract

AbstractFor a large class of partial differential equations on exterior domains or on ℝN we show that any solution tending to a limit from one side as x goes to infinity satisfies the property of “asymptotic spherical symmetry”. The main examples are semilinear elliptic equations, quasilinear degenerate elliptic equations, and first‐order Hamilton‐Jacobi equations.