6 papers
A maximum principle for the -Laplacian, an eigenvalue estimate and a stabilization phenomenon for the large- regime
Kevin Carrillo-Reina, Jean C. Cortissoz
We establish an explicit maximum principle for the Dirichlet problem associated with the -Laplacian (), where the constant depends on both and the geometry of the domai…
A Polyharmonic Liouville Hierarchy on Complete Manifolds of Nonnegative Ricci Curvature
John E. Bravo, Jean C. Cortissoz
In this paper, we establish a complete Liouville--type hierarchy for polyharmonic functions on Riemannian manifolds with nonnegative Ricci curvature. Extending Yau's classical resu…
On Liouville's theorem and the Strong Liouville Property
John E. Bravo, Jean C. Cortissoz
We explore Liouville's theorem and the Strong Liouville Property (SLP) for harmonic functions on Riemannian cones and surfaces. Our approach recasts the classical Liouville propert…
Liouville theorem for biharmonic functions on manifolds of nonnegative Ricci curvature
John E. Bravo, Jean C. Cortissoz
In this paper we extend Yau's celebrated Liouville theorem to the biharmonic case. Namely, we show that in a complete Riemannian manifold with a pole and nonnegative Ricci curvatur…
On sublinear elliptic systems on bounded and thin unbounded domains
Jean C. Cortissoz
In this paper, we demonstrate the existence of positive solutions for certain weakly coupled elliptic systems of sublinear growth under homogeneous Dirichlet boundary conditions. O…
On Milnor's criterion for deciding whether a surface is hyperbolic or parabolic for biharmonic functions
John E. Bravo, Jean C. Cortissoz
In this paper we generalise a celebrated result of Milnor that characterises whether a rotationally symmetric surface is parabolic or hyperbolic to the case of biharmonic functions…