15 papers
New definitions of a solution of a one-dimensional elliptic equation with a singular first order divergence term
Daniela Giachetti, Pedro Jesús MartÃnez-Aparicio, François Murat +1
In this paper, which is a continuation of our recent paper [1], we give two new definitions of a weak solution of the one-dimensional, elliptic, nonlinear singular problem which is…
Existence and non-existence phenomena for nonlinear elliptic equations with data and singular reactions
Francescantonio Oliva, Francesco Petitta, Matheus F. Stapenhorst
We study existence and non-existence of solutions for singular elliptic boundary value problems as \begin{equation}\label{eintro}\begin{cases}\tag{1} \displaystyle -Î_p u+ \frac{a…
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} -Îu + \frac{|\nabla u|^2}{(1-u)^γ}=g & \mbox{in ,}\newline \hf…
A duality approach to the fractional Laplacian with measure data
Kenneth H. Karlsen, Francesco Petitta, Suleyman Ulusoy
We describe a duality method to prove both existence and uniqueness of solutions to nonlocal problems like with vanishing conditi…
Diffuse measures and nonlinear parabolic equations
Francesco Petitta, Augusto C. Ponce, Alessio Porretta
Given a parabolic cylinder , where is a bounded domain, we prove new properties of solutions of \[ u_t-Î_p u = μ\quad \text{in } \…
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…