Examinando por Autor "Peral, Ireneo"

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    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.
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    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]).