This is a joint work with A. Salort and N. Wolanski. We continue our study of the large time behavior of the bounded solution to the nonlocal diffusion equation with absorption u t = Lu − u p in R N × (0, ∞), u(x, 0) = u 0 (x) in R N , where p > 1, u 0 ≥ 0 and bounded and Lu(x, t) = J(x − y) (u(y, t) − u(x, t)) dy with J ∈ C ∞ 0 (R N), radially symmetric, J… (More)
We review and extend some well known results for the eigenvalues of the Dirichlet p-Laplace operator to a more general class of monotone quasi-linear elliptic operators. As an application we obtain some homogenization results for nonlinear eigenvalues.
In this work we study the asymptotic distribution of eigenvalues in one-dimensional open sets. The method of proof is rather elementary, based on the Dirichlet lattice points problem, which enable us to consider sets with infinite measure. Also, we derive some estimates for the the spectral counting function of the Laplace operator on unbounded… (More)