In this article, we analyze the stability of the parallel surface problem for semilinear
equations driven by the fractional Laplacian. We prove a quantitative stability result that …

We study symmetry and quantitative approximate symmetry for an overdetermined problem
involving the fractional torsion problem in a bounded open set $\Omega\subset\mathbb R^ n …

In a bounded domain\varOmega Ω, we consider a positive solution of the problem Δ u+ f
(u)= 0 Δ u+ f (u)= 0 in\varOmega Ω, u= 0 u= 0 on ∂\varOmega∂ Ω, where f: R → R f: R→ R …

0 () depending only on the distance from the boundary of, then must be a ball. With some
restrictions on f, we prove that spherical symmetry can be obtained only by assuming that …

We use a Hopf-type lemma for antisymmetric super-solutions to the Dirichlet problem for the
fractional Laplacian with zero-th order terms, in combination with the method of moving …

We review classical results where the method of the moving planes has been used to prove
symmetry properties for overdetermined PDE's boundary value problems (such as Serrin's …

A positive solution of a homogeneous Dirichlet boundary value problem or initial-value
problems for certain elliptic or parabolic equations must be radially symmetric and monotone …

We consider nonlinear diffusion equations of the form∂ tu= Δϕ (u) in with N≥ 2. When ϕ
(s)≡ s, this is just the heat equation. Let Ω be a domain in, where∂ Ω is bounded and. We …

It is well known that the torsion function of a convex domain has a square root which is
concave. The power one half is optimal in the sense that no greater power ensures …

Let Ω be a domain in RN, where N⩾ 2 and∂ Ω is not necessarily bounded. We consider
nonlinear diffusion equations of the form∂ tu= Δϕ (u). Let u= u (x, t) be the solution of either …