175 citations · 729 across the 112 of their papers we have counts for
8 papers · 1 filter
Bubbling solutions for nonlocal elliptic problems
Juan Dávila, Luis López Ríos, Yannick Sire
We investigate bubbling solutions for the nonlocal equation \[ A_Ω^s u =u^p,\ u >0 \quad \mbox{in } Ω, \] under homogeneous Dirichlet conditions, where is a bounded and smooth…
A fractional isoperimetric problem in the Wiener space
Matteo Novaga, Diego Pallara, Yannick Sire
We introduce a notion of fractional perimeter in an abstract Wiener space, and we show that halfspaces are the only volume-constrained minimisers.
Nonlocal equations with measure data
Tuomo Kuusi, Giuseppe Mingione, Yannick Sire
We develop an existence, regularity and potential theory for nonlinear integrodifferential equations involving measure data. The nonlocal elliptic operators considered are possibly…
Construction of invariant whiskered tori by a parameterization method. Part II: Quasi-periodic and almost periodic breathers in coupled map lattices
Ernest Fontich, Rafael de la Llave, Yannick Sire
We construct quasi-periodic and almost periodic solutions for coupled Hamiltonian systems on an infinite lattice which is translation invariant. The couplings can be long range, pr…
A lower bound for the number of negative eigenvalues of Schrödinger operators
Alexander Grigor'yan, Nikolai Nadirashvili, Yannick Sire
We prove a lower bound for the number of negative eigenvalues for a Schrödinger operator on a Riemannian manifold via the integral of the potential.
Existence, Uniqueness and Asymptotic behaviour for fractional porous medium equations on bounded domains
Matteo Bonforte, Yannick Sire, Juan Luis Vazquez
We consider nonlinear diffusive evolution equations posed on bounded space domains, governed by fractional Laplace-type operators, and involving porous medium type nonlinearities.…