Currently displaying 1 – 6 of 6

Showing per page

Order by Relevance | Title | Year of publication

Interpolation theorem for the p-harmonic transform

Luigi D'OnofrioTadeusz Iwaniec — 2003

Studia Mathematica

We establish an interpolation theorem for a class of nonlinear operators in the Lebesgue spaces s ( ) arising naturally in the study of elliptic PDEs. The prototype of those PDEs is the second order p-harmonic equation d i v | u | p - 2 u = d i v . In this example the p-harmonic transform is essentially inverse to d i v ( | | p - 2 ) . To every vector field q ( , ) our operator p assigns the gradient of the solution, p = u p ( , ) . The core of the matter is that we go beyond the natural domain of definition of this operator. Because of nonlinearity our arguments...

On weak Hessian determinants

Luigi D'OnofrioFlavia GiannettiLuigi Greco — 2005

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We consider and study several weak formulations of the Hessian determinant, arising by formal integration by parts. Our main concern are their continuity properties. We also compare them with the Hessian measure.

Divergence forms of the infinity-Laplacian.

Luigi D'OnofrioFlavia GiannettiTadeusz IwaniecJuan ManfrediTeresa Radice — 2006

Publicacions Matemàtiques

The central theme running through our investigation is the infinity-Laplacian operator in the plane. Upon multiplication by a suitable function we express it in divergence form, this allows us to speak of weak infinity-harmonic function in W1,2. To every infinity-harmonic function u we associate its conjugate function v. We focus our attention to the first order Beltrami type equation for h= u + iv

On the continuity of minimizers for quasilinear functionals

David Cruz-UribePatrizia Di GironimoLuigi D'Onofrio — 2012

Czechoslovak Mathematical Journal

In this paper we establish a continuity result for local minimizers of some quasilinear functionals that satisfy degenerate elliptic bounds. The non-negative function which measures the degree of degeneracy is assumed to be exponentially integrable. The minimizers are shown to have a modulus of continuity controlled by log log ( 1 / | x | ) - 1 . Our proof adapts ideas developed for solutions of degenerate elliptic equations by J. Onninen, X. Zhong: Continuity of solutions of linear, degenerate elliptic equations, Ann....

Page 1

Download Results (CSV)