Examinando por Autor "Primo, Ana"

Mostrando 1 - 4 de 4
  • Miniatura
    Publicación
    Basic estimates for solutions of a class of nonlocal elliptic and parabolic equations
    (American Institute of Mathematical Sciences (AIMS), 2015-12) Leonori, Tommaso; Peral, Ireneo; Primo, Ana; Soria, Fernando; https://orcid.org/0000-0002-0848-4463; https://orcid.org/0000-0003-2297-9910; https://orcid.org/0000-0003-1804-3175; https://orcid.org/0000-0001-5753-807X
    In this work we consider the problems { script Lu = f in Ω, u = 0 in ℝN\Ω, and { ut + script Lu = f in QT ≡ Ω x (0,T), u(x,t) = 0 in (ℝN\Ω) x (0,T), u(x, 0) = 0 in Ω, where script L is a nonlocal differential operator and Ω is a bounded domain in ℝN, with Lipschitz boundary. The main goal of this work is to study existence, uniqueness and summability of the solution u with respect to the summability of the datum f. In the process we establish an Lp-theory, for p ≥ 1, associated to these problems and we prove some useful inequalities for the applications.
  • Miniatura
    Publicación
    Existence of solutions for semilinear nonlocal elliptic problems via a Bolzano theorem
    (Springer-Verlag, 2013-10-01) Arcoya, David; Leonori, Tommaso; Primo, Ana; https://orcid.org/0000-0002-7284-2413; https://orcid.org/0000-0002-0848-4463; https://orcid.org/0000-0003-1804-3175
    In this paper we deal with the existence of positive solutions for the following nonlocal type of problems {-Δu = α/(σωg(u)dx) p f(u) in Ω u>0 in Ω u=0 on ∂ Ω where Ω is a bounded smooth domain in ℝ N (N≥1), f,g are continuous positive functions, σ>0 and pεℝ. We give sufficient conditions on the functions f and g in order to have existence of positive solutions.
  • Miniatura
    Publicación
    Nonlinear elliptic equations with Hardy potential and lower order term with natural growth
    (Elsevier, 2011-07) Leonori, Tommaso; Martínez-Aparicio, Pedro J.; Primo, Ana
    In this work we analyze the interaction between the Hardy potential and a lower order term to obtain the existence or nonexistence of a positive solution in elliptic problems whose model is {-Δpu=g(u)| ∇u| p+λ up-1/|x|p +f,in Ω,u>0,in Ω,u=0,on ∂Ω, where ΩℝN, N≥3, is a bounded domain containing the origin, 10, the behavior of the positive continuous function g at infinity provides the existence of a solution for such a problem.
  • Miniatura
    Publicación
    Principal eigenvalue of mixed problem for the fractional Laplacian: Moving the boundary conditions
    (Elsevier, 2018-07-15) Leonori, Tommaso; Medina, Maria; Peral, Ireneo; Primo, Ana; Soria, Fernando
    We analyze the behavior of the eigenvalues of the following nonlocal mixed problem {(−Δ)su=λ1(D)u in Ω,u=0 in D,Nsu=0 in N. Our goal is to construct different sequences of problems by modifying the configuration of the sets D and N, and to provide sufficient and necessary conditions on the size and the location of these sets in order to obtain sequences of eigenvalues that in the limit recover the eigenvalues of the Dirichlet or Neumann problem. We will see that the nonlocality plays a crucial role here, since the sets D and N can have infinite measure, a phenomenon that does not appear in the local case (see for example [6–8]).