Showing papers by "Ariel Martin Salort published in 2022"

Asymptotic behavior for anisotropic fractional energies

Abstract: . In this paper we investigate the asymptotic behavior of anisotropic fractional energies as the fractional parameter s ∈ (0 , 1) approaches both s ↑ 1 and s ↓ 0 in the spirit of the celebrated papers of Bourgain-Brezis-Mironescu [6] and Maz’ya-Shaposhnikova [20]. Then, focusing con the case s ↑ 1 we analyze the behavior of solutions to the corresponding minimization problems and finally, we also study the problem where a homogenization effect is combined with the localization phenomena that occurs when s ↑ 1.

Homogeneous eigenvalue problems in Orlicz-Sobolev spaces

Abstract: . In this article we consider a homogeneous eigenvalue problem ruled by the fractional g − Laplacian operator whose Euler-Lagrange equation is obtained by minimization of a quotient involving Luxemburg norms. We prove existence of an infinite sequence of variational eigenvalues and study its behavior as the fractional parameter s ↑ 1 among other stability results.

Rotating Spirals in segregated reaction-diffusion systems

Abstract: We give a complete characterization of the boundary traces φi (i = 1, . . . , K) supporting spiraling waves, rotating with a given angular speed ω, which appear as singular limits of competition-diffusion systems of the type  ∂tui − ∆ui = μui − βui ∑j 6=i aijuj in Ω×R+ ui = φi on ∂Ω×R+ ui(x, 0) = ui,0(x) for x ∈ Ω as β → +∞. Here Ω is a rotationally invariant planar set and aij > 0 for every i and j. We tackle also the homogeneous Dirichlet and Neumann boundary conditions, as well as entire solutions in the plane. As a byproduct of our analysis we detect explicit families of eternal, entire solutions of the pure heat equation, parameterized by ω ∈ R, which reduce to homogeneous harmonic polynomials for ω = 0.