Begoña Barrios

Some remarks on the solvability of non-local elliptic problems with the Hardy potential

The aim of this paper is to study the solvability of the following problem, where (-Δ)s, with s ∈ (0, 1), is a fractional power of the positive operator -Δ, Ω ⊂ ℝN, N > 2s, is a Lipschitz bounded domain such that 0 ∈ Ω, μ is a positive real number, λ < ΛN,s, the sharp constant of the Hardy–Sobolev inequality, 0 < q < 1 and , with αλ a parameter depending on λ and satisfying . We will discuss the existence and multiplicity of solutions depending on the value of p, proving in particular that p(λ, s) is the threshold for the existence of solution to problem (Pμ).

A Widder’s Type Theorem for the Heat Equation with Nonlocal Diffusion

AbstractThe main goal of this work is to prove that every non-negative strong solutionu(x, t) to the problem

On the moving plane method for nonlocal problems in bounded domains

u_t + (-\Delta)^{\alpha/2}{u} = 0 \,\, {\rm for} (x, t) \in {\mathbb{R}^n} \times (0, T ), \, 0 < \alpha < 2,

On some critical problems for the fractional Laplacian operator

ut+(-Δ)α/2u=0for(x,t)∈Rn×(0,T),0<α<2,can be written as

Some remarks about the summability of nonlocal nonlinear problems

u(x, t) = \int_{\mathbb{R}^n} P_t (x - y)u(y, 0) dy,

Neumann conditions for the higher order

u(x,t)=∫RnPt(x-y)u(y,0)dy,where