4 papers · 1 filter
A nonlinear elliptic problem involving the gradient on a half space
A. Aghajani, C. Cowan, S. H. Lui
We consider perturbations of the diffusive Hamilton-Jacobi equation \begin{equation*} %\label{non_pert} \left\{ \begin{array}{lcl} \hfill -Δu &=& (1+g(x))| \nabla u|^p\qquad \mbox{…
Some elliptic problems involving the gradient on general bounded and exterior domains
A. Aghajani, C. Cowan
In this article we consider the existence of positive singular solutions on bounded domains and also classical solutions on exterior domains. First we consider positive singular so…
A note on the nonexistence of positive supersolutions to elliptic equations with gradient terms
A. Aghajani, C. Cowan
We prove that if the elliptic problem with has a positive supersolution in a domain of $ \IR^{N\ge 3}$, then must satisfy the inequalit…
Explicit estimates on positive supersolutions of nonlinear elliptic equations and applications
A. Aghajani, C. Cowan
In this paper we consider positive supersolutions of the nonlinear elliptic equation \[- Δu = ρ(x) f(u)|\nabla u|^p, \qquad \hfill \mbox{ in } Ω,\] where , is an arb…