Francesco Petitta
University of Valencia
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Comptes Rendus Mathematique | 2007
Francesco Petitta
Abstract In this Note we deal with the asymptotic behavior as t tends to infinity of solutions for linear parabolic equations whose model is { u t − Δ u = μ in ( 0 , T ) × Ω , u ( 0 , x ) = u 0 in Ω , where μ is a general, possibly singular, Radon measure which does not depend on time, and u 0 ∈ L 1 ( Ω ) . We prove that the duality solution, which exists and is unique, converges to the duality solution (as introduced by Stampacchia (1965)) of the associated elliptic problem. To cite this article: F. Petitta, C. R. Acad. Sci. Paris, Ser. I 344 (2007).
Publicacions Matematiques | 2011
Kenneth H. Karlsen; Francesco Petitta; Suleyman Ulusoy
We describe a duality method to prove both existence and uniqueness of solutions to nonlocal problems like ( ) s v = in R N ; with vanishing conditions at innity. Here is a bounded Radon measure whose support is compactly contained in R N , N 2, and () s is the fractional Laplace operator of order s2 (1=2; 1).
ESAIM: Control, Optimisation and Calculus of Variations | 2016
Francescantonio Oliva; Francesco Petitta
We prove existence of solutions for a class of singular elliptic problems with a general measure as source term whose model is \begin{eqnarray} \begin{cases} \dys -\Delta u = \frac{f(x)}{u^{\gamma}} +\mu & \text{in}\ \Omega,\\[2mm] u=0 &\text{on}\ \partial\Omega,\\[2mm] u>0 &\text{on}\ \Omega, \end{cases} \end{eqnarray} where Ω is an open bounded subset of ℝ N . Here γ > 0, f is a nonnegative function on Ω , and μ is a nonnegative bounded Radon measure on Ω .
Calculus of Variations and Partial Differential Equations | 2011
Tommaso Leonori; Francesco Petitta
In this paper we deal with local estimates for parabolic problems in
Journal of Differential Equations | 2018
Francescantonio Oliva; Francesco Petitta
Advanced Nonlinear Studies | 2016
Francesco Petitta
{\mathbb{R}^N}
arXiv: Analysis of PDEs | 2015
Francesco Petitta; Alessio Porretta
Communications in Partial Differential Equations | 2017
Lorenzo Giacomelli; Salvador Moll; Francesco Petitta
with absorbing first order terms, whose model is
Journal D Analyse Mathematique | 2015
Salvador Moll; Francesco Petitta
arXiv: Analysis of PDEs | 2009
Francesco Petitta
\left\{\begin{array}{l@{\quad}l}u_t- \Delta u +u |\nabla u|^q = f(t,x) \quad &{\rm in}\, (0,T) \times \mathbb{R}^N\,,\\u(0,x)= u_0 (x) &{\rm in}\, \mathbb{R}^N \,,\quad\end{array}\right.