106 citations · 147 across the 15 of their papers we have counts for
15 papers
Quasilinear elliptic equations with singular quadratic growth terms
Lucio Boccardo, Tommaso Leonori, Luigi Orsina +1
In this paper we deal with positive solutions for singular quasilinear problems whose model is $$ \begin{cases} -Δu + \frac{|\nabla u|^2}{(1-u)^γ}=g & \mbox{in ,}\newline \hfill…
Existence and nonexistence of solutions for singular quadratic quasilinear equations
David Arcoya, José Carmona, Tommaso Leonori +3
We study both existence and nonexistence of nonnegative solutions for nonlinear elliptic problems with singular lower order terms that have natural growth with respect to the gradi…
On maximal regularity estimates for quasilinear evolution equations via the integral Bernstein method
Alessandro Goffi, Tommaso Leonori
This work addresses the problem of (global) maximal regularity for quasilinear evolution equations with sublinear gradient growth and right-hand side in Lebesgue spaces, complement…
The best approximation of a given function in -norm by Lipschitz functions with gradient constraint
Stefano Buccheri, Tommaso Leonori, Julio D. Rossi
The starting point of this paper is the study of the asymptotic behavior, as , of the following minimization problem $$ \min\left\{\frac1{p}\int|\nabla v|^{p}+\frac12\i…
Gradient estimates for quasilinear elliptic Neumann problems with unbounded first-order terms
Marco Cirant, Alessandro Goffi, Tommaso Leonori
This paper studies global a priori gradient estimates for divergence-type equations patterned over the -Laplacian with first-order terms having polynomial growth with respect to…
Deterministic KPZ-type equations with nonlocal "gradient terms"
Boumediene Abdellaoui, Antonio J. Fernández, Tommaso Leonori +1
The main goal of this paper is to prove existence and non-existence results for deterministic Kardar-Parisi-Zhang type equations involving non-local "gradient terms". More precisel…
Global fractional Calderón-Zygmund type regularity
Boumediene Abdellaoui, Antonio J. Fernández, Tommaso Leonori +1
We obtain a global fractional Calderón-Zygmund regularity theory for the fractional Poisson problem. More precisely, for , , a bounded domain with…
Regularity of solutions to a fractional elliptic problem with mixed Dirichlet-Neumann boundary data
J. Carmona, E. Colorado, T. Leonori +1
In this work we study regularity properties of solutions to fractional elliptic problems with mixed Dirichlet-Neumann boundary data when dealing with the Spectral Fractional Laplac…
Semilinear fractional elliptic problems with mixed Dirichlet-Neumann boundary conditions
J. Carmona, E. Colorado, T. Leonori +1
We study a nonlinear elliptic boundary value problem defined on a smooth bounded domain involving the fractional Laplace operator, a concave-convex powers term together with mixed…
Comparison results for unbounded solutions for a parabolic Cauchy-Dirichlet problem with superlinear gradient growth
Tommaso Leonori, Martina Magliocca
In this paper we deal with uniqueness of solutions to the following problem \[ \begin{cases} \begin{split} & u_t-Δ_p u=H(t,x,\nabla u) &\quad \text{in}\quad Q_T,\\ & u (t,x) =0 &\q…
Principal Eigenvalue of Mixed Problem for the Fractional Laplacian: Moving the Boundary Conditions
Tommaso Leonori, Maria Medina, Ireneo Peral +2
We analyze the behavior of the eigenvalues of the following non local mixed problem $\left\{ \begin{array}{rcll} (-Δ)^{s} u &=& λ_1(D) \ u &\innΩ,\\ u&=&0&\inn D,\\ \mathcal{N}_{s}…
Parabolic equations with natural growth approximated by nonlocal equations
Tommaso Leonori, Alexis Molino, Sergio Segura de León
In this paper we study several aspects related with solutions of nonlocal problems whose prototype is $$ u_t =\displaystyle \int_{\mathbb{R}^N} J(x-y) \big( u(y,t) -u(x,t) \big) \m…
Local estimates for parabolic equations with nonlinear gradient terms
Tommaso Leonori, Francesco Petitta
In this paper we deal with local estimates for parabolic problems in with absorbing first order terms, whose model is $\{ {l} u_t- Δu +u |\nabla u|^q = f(t,x) \quad…
Ground states of self-gravitating elastic bodies
Simone Calogero, Tommaso Leonori
The existence of static, self-gravitating elastic bodies in the non-linear theory of elasticity is established. Equilibrium configurations of self-gravitating elastic bodies close…
Growth conditions and uniqueness of the Cauchy problem for the evolutionary infinity Laplacian
Tommaso Leonori, José Miguel Urbano
We study the Cauchy problem for the parabolic infinity Laplace equation. We prove a new comparison principle and obtain uniqueness of viscosity solutions in the class of functions…