Examinando por Autor "Leonori, Tommaso"
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Publicación Asymptotically Linear Problems and Antimaximum Principle for the Square Root of the Laplacian(2016-03-10) Arcoya, David; Colorado, Eduardo; Leonori, Tommaso; https://orcid.org/0000-0002-7284-2413; https://orcid.org/0000-0002-1067-5752; https://orcid.org/0000-0002-0848-4463This work deals with bifurcation of positive solutions for some asymptotically linear problems, involving the square root of the Laplacian (-Delta)(1/2). A simplified model problem is the following: {(-Delta)(1/2)u = lambda m(x)u + g(u) in Omega, u = 0 on partial derivative Omega, with Omega subset of R-N a smooth bounded domain, N >= 2, lambda > 0, m is an element of L-infinity(Omega), m(+) not equivalent to 0 and g is a continuous function which is super-linear at 0 and sub-linear at infinity. As a consequence of our bifurcation theory approach we prove some existence and multiplicity results. Finally, we also show an anti-maximum principle in the corresponding functional setting.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/0000-0001-5753-807XIn 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.Publicación The best approximation of a given function in L2-norm by Lipschitz functions with gradient constraint(De Gruyter, 2024-04-24) Buccheri, Stefano; Leonori, Tommaso; Rossi, Julio D.; https://orcid.org/0000-0002-0667-233X; https://orcid.org/0000-0002-0848-4463; https://orcid.org/0000-0002-5905-4412Publicación Comparison principles for p-Laplace equations with lower order terms(Springer Nature, 2016-08-06) Leonori, Tommaso; Porretta, Alessio; Riey, GiuseppeWe prove comparison principles for quasilinear elliptic equations whose simplest model is (Formula presented.), where Δpu=div(|Du|p-2Du) is the p-Laplace operator with p> 2 , λ≥ 0 , H(x, ξ) : Ω × RN→ R is a Carathéodory function and Ω ⊂ RN is a bounded domain, N≥ 2. We collect several comparison results for weak sub- and super-solutions under different setting of assumptions and with possibly different methods. A strong comparison result is also proved for more regular solutions.Publicación Comparison results for unbounded solutions for a parabolic Cauchy-Dirichlet problem with superlinear gradient growth(American Institute of Mathematical Sciences (AIMS), 2019-05) Leonori, Tommaso; Magliocca, MartinaIn this paper we deal with uniqueness of unbounded solutions to the following problem (formula pergented) where QT = (0, T) × Ω is the parabolic cylinder, Ω is an open subset of RN, N ≥ 2, 1 < p < N, and the right hand side H(t, x, ξ): (0, T) × Ω × RN → R exhibits a superlinear growth with respect to the gradient term. © 2019 American Institute of Mathematical Sciences.Publicación Deterministic KPZ-type equations with nonlocal “gradient terms”(Springer Nature, 2023-12-03) Abdellaou, Boumediene; Fernández, Antonio J.; Leonori, Tommaso; Younes, Abdelbadie; https://orcid.org/0000-0002-0848-4463; https://orcid.org/0000-0001-6236-2769Publicación 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/0000-0003-1804-3175In 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.Publicación Ground states of self-gravitating elastic bodies(Springer Nature, 2014-09) Calogero, Simone; Leonori, Tommaso; https://orcid.org/0000-0003-3802-3665; https://orcid.org/0000-0002-0848-4463The existence of static, self-gravitating elastic bodies in the non-linear theory of elasticity is established. Equilibrium configurations of self-gravitating elastic bodies close to the reference configuration have been constructed in Beig and Schmidt (Proc R Soc Lond, 109–115, 2003) using the implicit function theorem. In contrast, the steady states considered in this article correspond to deformations of the relaxed state with no size restriction and are obtained as minimizers of the energy functional of the elastic body.Publicación Large solutions and gradient bounds for quasilinear elliptic equations(Taylor and Francis Group, 2015-10-09) Leonori, Tommaso; Porretta, AlessioWe consider the quasilinear degenerate elliptic equation λu - Δpu + H(x,Du)= 0 in Ω where Δp is the p-Laplace operator, p > 2, λ ≥0 and Ω is a smooth open bounded subset of ℝN (N ≥ 2). Under suitable structure conditions on the function H, we prove local and global gradient bounds for the solutions. We apply these estimates to study the solvability of the Dirichlet problem, and the existence, uniqueness and asymptotic behavior of maximal solutions blowing up at the boundary. The ergodic limit for those maximal solutions is also studied and the existence and uniqueness of a so-called additive eigenvalue is proved in this context.Publicación Large solutions to quasilinear problems involving the p-Laplacian as p diverges(Springer Nature, 2021-01-18) Buccheri, Stefano; Leonori, TommasoPublicación On the comparison principle for unbounded solutions of elliptic equations with first order terms(Elsevier, 2018-01-15) Leonori, Tommaso; Porretta, AlessioWe prove a comparison principle for unbounded weak sub/super solutions of the equation λu−div(A(x)Du)=H(x,Du) in Ω where A(x) is a bounded coercive matrix with measurable ingredients, λ≥0 and ξ↦H(x,ξ) has a super linear growth and is convex at infinity. We improve earlier results where the convexity of H(x,⋅) was required to hold globally.Publicación Parabolic equations with natural growth approximated by nonlocal equations(World Scientific, 2021) Leonori, Tommaso; Molino, Alexis; Segura De León, Sergio; https://orcid.org/0000-0002-0848-4463; https://orcid.org/0000-0003-2819-7282; https://orcid.org/0000-0002-8515-7108Publicación 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, FernandoWe 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]).Publicación Regularity of solutions to a fractional elliptic problem with mixed Dirichlet-Neumann boundary data(De Gruyter, 2021-10-01) Carmona, Jose; Colorado, Eduardo; Leonori, Tommaso; Ortega, Alejandro; 35996792500; 6507374993; 14521092300; 56489711800In this work we study regularity properties of solutions to fractional elliptic problems with mixed Dirichlet-Neumann boundary data when dealing with the spectral fractional Laplacian.Publicación Semilinear fractional elliptic problems with mixed Dirichlet-Neumann boundary conditions(Elsevier, 2020-08-01) Carmona, José; Colorado, Eduardo; Leonori, Tommaso; Ortega, Alejandro; 6507374993; 14521092300; 56489711800We study a nonlinear elliptic boundary value problem defined on a smooth bounded domain involving the fractional Laplace operator and a concave-convex term, together with mixed Dirichlet-Neumann boundary conditions.Publicación Strong convergence of the gradients for p-Laplacian problems as p → ∞(Elsevier, 2021-03-01) Buccheri, Stefano; Leonori, Tommaso; Rossi, Julio D.In this paper we prove that the gradients of solutions to the Dirichlet problem for −∆pup = f , with f > 0, converge as p → ∞ strongly in every Lq with 1 ≤ q < ∞ to the gradient of the limit function. This convergence is sharp since a simple example in 1-d shows that there is no convergence in L∞. For a nonnegative f we obtain the same strong convergence inside the support of f . The same kind of result also holds true for the eigenvalue problem for a suitable class of domains (as balls or stadiums).Publicación W01,1 -solutions for elliptic problems having gradient quadratic lower order terms(Springer Nature, 2013-04-10) David, Arcoya; Boccardo, Lucio; Leonori, Tommaso; https://orcid.org/0000-0002-7284-2413; https://orcid.org/0000-0002-8067-0121; https://orcid.org/0000-0002-0848-4463In this paper we deal with solutions of problems of the type (Formula presented). where 0 < α ≤ a(x) ≤ β, {pipe}b(x){pipe} ≤ γ, γ > 0, f ∈ L2 (Ω) and Ω is a bounded subset of ℝN with N ≥ 3. We prove the existence of at least one solution for such a problem in the space W01,1 (Ω) ∩ L2 (Ω) if the size of the lower order term satisfies a smallness condition when compared with the principal part of the operator. This kind of problems naturally appears when one looks for positive minima of a functional whose model is: (Formula presented). where in this case a(x) ≡ b(x) = α > 0.