Separable -harmonic functions in a cone and related quasilinear equations on manifolds
Singular functions on metric measure spaces.
On relatively compact domains in metric measure spaces we construct singular functions that play the role of Green functions of the p-Laplacian. We give a characterization of metric spaces that support a global version of such singular function, in terms of capacity estimates at infinity of such metric spaces. In addition, when the measure of the space is locally Q-regular, we study quasiconformal invariance property associated with the existence of global singular functions.
Solving -Laplacian equations on complete manifolds.
Some non-linear function theoretic properties of Riemannian manifolds.
We study the appropriate versions of parabolicity stochastic completeness and related Liouville properties for a general class of operators which include the p-Laplace operator, and the non linear singular operators in non-diagonal form considered by J. Serrin and collaborators.
Stability and Continuity of Functions of Least Gradient
In this note we prove that on metric measure spaces, functions of least gradient, as well as local minimizers of the area functional (after modification on a set of measure zero) are continuous everywhere outside their jump sets. As a tool, we develop some stability properties of sequences of least gradient functions. We also apply these tools to prove a maximum principle for functions of least gradient that arise as solutions to a Dirichlet problem.
Superharmonic functions and differential equations involving measures for quasilinear elliptic operators with lower order terms.
Sur la représentation par les lois de sortie.