The Quasiworld

I received my Ph. D. from Washington University in St. Louis in 1986 under the direction of Albert Baernstein II. I work on the partial differential equations that govern the non linear potential theory of quasi-regular mappings in higher dimensions, their subelliptic extensions, and their game theoretic interpreations.

Juan J. Manfredi Department of Mathematics University of Pittsburgh Pittsburgh, PA 15260-0001 e-mail address: manfredi at pitt.edu

Other Worlds:

Carl Gustav Axel Harnak World.

Here is some material from recent talks:

Jyväskylä Summer School, August 2005.
Heisenberg Mathematica notebook Geodesics Mathematica notebook
Regularity of p-harmonic functions in Euclidean spaces and Heisenberg groups presented at the conference THE p-LAPLACE EQUATION, THE INFINITY-LAPLACE EQUATION AND RELATED TOPICS in honor of Gunnar Aronsson, Linköping University, October 2004.
Notes from a course I gave in Trento's Third School on Analysis and Geometry in Metric Spaces in May 2003: Nonlinear Subelliptic Equations on Carnot Groups.
Vicosity solutions of the p-Laplace equation. presented at EPSRC Gregynog 02 Workshop on Computation and Analytic Problems in Spectral Theory

Below are some of my recent publications.

A complete list is at Manfredi publications . My citations are at Manfredi Citations (MathSci subscription needed).

Sharp Global Bounds for the Hessian on Pseudo-Hermitian Manifolds.
Written in collaboration with Sagun Chanillo.
To appear in a volume in honor of Carlos Segovai, edited by Cabrelli and Torrea. Equations.
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pdf
Viscosity Supersolutions of the Evolutionary p-Laplace Equation.
Written in collaboration with Peter Lindqvist.
To appear in the Journal of Integral and Differential Equations.
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pdf
Note on a Remarkable Superposition for a Nonlinear Equation.
Written in collaboration with Peter Lindqvist.
To appear in the Proceedings of the American Mathematical Society.
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pdf
The Neumann Problem for the infinity Laplacian and the Monge-Kantorovich Mass Transfer Problem.
Written in collaboration with J. Garcia-Azorero, I. Peral, and J. Rossi.
Nonlinear Analysis: Theory, Methods and Applications 66 (2) (2007), 349-366.
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pdf
Subelliptic Cordes Estimates in the Grushin Plane.
Written in collaboration with G. Di Fazio, A. Domokos, and M.S. Fanciullo.
Manuscripta Mathematica 120 (4) (2006), 419-433.
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pdf
Quasilinear Elliptic Equations in the Heisenberg group.
Written in collaboration with Giuseppe Mingione.
2007 Mathematische Annalen.
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pdf
p-Harmonic Measure is not Subadditive.
Written in collaboration with Jose G. Llorente and Jang-Mei Wu.
Annalli della Scuola Normale Superiore di Pisa, Classe di Scienze IV (5) (2005), 357-373.
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pdf
Subelliptic Cordes Estimates.
Written in collaboration with Andras Domokos.
Proceedings of the American Mathematical Society 133 (2005), 1047--1056.
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pdf
Rearrangements in Carnot Groups.
Written in collaboration with Virginia Vera de Serio. We prove a version of the Polya-Szego symmetrization principle valid in general Carnot groups.
Working Draft welcome.
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pdf

The Quasiworld

Jyväskylä Summer School, August 2005.

Regularity of p-harmonic functions in Euclidean spaces and Heisenberg groups presented at the conference THE p-LAPLACE EQUATION, THE INFINITY-LAPLACE EQUATION AND RELATED TOPICS in honor of Gunnar Aronsson, Linköping University, October 2004.

Notes from a course I gave in Trento's Third School on Analysis and Geometry in Metric Spaces in May 2003: Nonlinear Subelliptic Equations on Carnot Groups.

Vicosity solutions of the p-Laplace equation. presented at EPSRC Gregynog 02 Workshop on Computation and Analytic Problems in Spectral Theory

Sharp Global Bounds for the Hessian on Pseudo-Hermitian Manifolds.

Viscosity Supersolutions of the Evolutionary p-Laplace Equation.

Note on a Remarkable Superposition for a Nonlinear Equation.

The Neumann Problem for the infinity Laplacian and the Monge-Kantorovich Mass Transfer Problem.

Subelliptic Cordes Estimates in the Grushin Plane.

Quasilinear Elliptic Equations in the Heisenberg group.

p-Harmonic Measure is not Subadditive.

Subelliptic Cordes Estimates.

Rearrangements in Carnot Groups.