A remark on -harmonic functions on Riemannian manifolds.
A remark on infinity harmonic functions.
A remark on some nonlinear elliptic problems.
A result on the bifurcation from the principal eigenvalue of the -Laplacian.
A semi-smooth Newton method for solving elliptic equations with gradient constraints
Semi-smooth Newton methods for elliptic equations with gradient constraints are investigated. The one- and multi-dimensional cases are treated separately. Numerical examples illustrate the approach and as well as structural features of the solution.
A semi-smooth Newton method for solving elliptic equations with gradient constraints
Semi-smooth Newton methods for elliptic equations with gradient constraints are investigated. The one- and multi-dimensional cases are treated separately. Numerical examples illustrate the approach and as well as structural features of the solution.
A strongly degenerate quasilinear equation : the elliptic case
We prove existence and uniqueness of entropy solutions for the Neumann problem for the quasilinear elliptic equation , where , , and is a convex function of with linear growth as , satisfying other additional assumptions. In particular, this class includes the case where , , being a convex function with linear growth as . In the second part of this work, using Crandall-Ligget’s iteration scheme, this result will permit us to prove existence and uniqueness of entropy solutions for the...
A weak maximum principle and estimates of for nonlinear degenerate elliptic equations
A weighted isoperimetric inequality and applications to symmetrization.
Absence of positive eigenvalues for a class of subelliptic operators.
𝒞1,β regularity for Dirichlet problems associated to fully nonlinear degenerate elliptic equations
We prove Hölder regularity of the gradient, up to the boundary for solutions of some fully-nonlinear, degenerate elliptic equations, with degeneracy coming from the gradient.
An approximation theorem for solutions of degenerate semilinear elliptic equations
The main result establishes that a weak solution of degenerate semilinear elliptic equations can be approximated by a sequence of solutions for non-degenerate semilinear elliptic equations.
An eigenvalue problem related to Hardy’s inequality
An elementary proof of the Harnack inequality for non-negative infinity-superharmonic functions.
An existence and approximation theorem for solutions of degenerate quasilinear elliptic equations
The main result establishes that a weak solution of degenerate quasilinear elliptic equations can be approximated by a sequence of solutions for non-degenerate quasilinear elliptic equations.
An index formula for the degree of (S)-mappings associated with one-dimensional -Laplacian.
An infinite-harmonic analogue of a Lelong theorem and infinite-harmonicity cells.
An integro-differential inequality related to the smallest positive eigenvalue ofp(x)-Laplacian Dirichlet problem
We consider the eigenvalue problem for the p(x)-Laplace-Beltrami operator on the unit sphere. We prove same integro-differential inequalities related to the smallest positive eigenvalue of this problem.
Analyse précisée d'équations semi-linéaires elliptiques sur l'espace hyperbolique et application à la courbure scalaire conforme
Analyse sur les boules d' un opérateur sous-elliptique.