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 and their subelliptic extensions.

 
 Juan J. Manfredi
 Department of Mathematics
 University of Pittsburgh
 Pittsburgh, PA 15260-0001

voice:		(412) 624 83 74
office:  	(412) 624 83 75
fax:	 	(412) 624 83 97
mobile:         (412) 726 73 80
e-mail address:
manfredi@pitt.edu

Other Worlds:

Carl Gustav Axel Harnak World.

Here are some of my recent talks:

Vicosity solutions of the p-Laplace equation. presented at EPSRC Gregynog 02 Workshop on Computation and Analytic Problems in Spectral Theory
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.
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.
Jyväskylä Summer School, August 2005.
Heisenberg Mathematica notebook
Geodesics Mathematica notebook

Here are some of my recent publications:

The Harnack Inequality for infinite-harmonic functions
Written in collaboration with Peter Lindqvist.
Electronic Journal of Differential Equations 44, 1995.

View Article directly from EJDE:
EJDE
Quasiregular Mappings from the Multilinear Point of View.
These are my notes from the 1994 Fall Shool of Analysis at the University of Jyväskylä. They are published by the University of Jyväskylä. Here is the complete reference:
Ber. Univ. Jyväskylä Math. Inst. 68 (1995), pp. 55-94.
These notes contain an introducion to the theory of quasiregular mappings based on the Iwaniec-Martin-Donaldson-Sullivan theory, suitable for beginners. Prerequisites include only basic real and complex analysis.
Thanks to everyone that sent missprints. If you find some more, please drop me a line. Latest version posted on September 4, 1996.

View Article:
DVI
Regularity Theory and Traces for A-harmonic Functions
Written in collaboration with Enrique Villlamor and Pekka Koskela.
Transactions of the American Mathematical Sociey 348 (1996), 755-766.

View Article directly from the AMS
TAMS
Mappings with Integrable Dilatation in Higher Dimensions
Written in collaboration with my friend Enrique Villamor.
Bulletin of the Amer. Math. Soc. 32(2), 1995, pp. 235-240.

View Article:
View Article directly from the AMS

In this paper we do some computer calculations. If you want to see the details, here they are in the form of a Mathematica 2.2 notebook

An extension of Reshetnyak's Theorem
Also written in collaboration with Enrique. This article contains all the details missing in the above announcement.
Indiana Journal of Mathematics 47(3), 1998, 1131-1146.

View Article:
DVI
Note on infinite-superharmonic functions
Written in collaboration with Peter Lindqvist.
Revista Matemática de la Universidad Complutense de Madrid 10(2), 1997, 1-9.

View Article:
DVI
The infinite-Eigenvalue Problem
Written in collaboration with Petri Juutinen and Peter Lindqvist.
Archive for Rational Mechanics and Analysis 148(1999), pp. 89-105.

View Article:
DVI
Traces of Monotone Functions on Weighted Sobolev Classes
Written in collaboration with Enrique Villamor.
To appear in the Illinois Journal of Mathematics

View Article (Revised version March 2001):
pdf
Sobolev versus Hölder Local Minimizers and Global Multiplicity for some Quasilinear Elliptic Equations
Written in collaboration with Jesús García-Azorero and Ireneo Peral.
Communications in Contemporary Mathematics, Vol 2(3), pp. 385-404, 2000.

View Article:
DVI
Superharmonicity of Nonlinear Ground States
Written in collaboration with Peter Lindqvist and Eero Saksman.
Revista Iberoamericana de Matemáticas, Vol 16(1), pp. 17-28, 2000

View Article:
dvi
A Version of the Hopf-Lax formula in the Heisenberg Group.
Written in collaboration with Bianca Stroffolini.
Communications in PDE 27(5& 6), 1139-1159 (2002).
View article:
pdf
Viscosity Solutions of the p-Laplace equation.
Written in collaboration with Petri Juutinen.
Proceedings on Analysis and Geometry, Novosibirsk Akademgorodok, Izdat. Ross. Akad. Nauk Sib. Otd. Inst. Mat., Novosibirsk, 2000, pp. 273--217.
View Article:
dvi
On the Equivalence of Viscosity Solutions and Weak Solutions for a Quasilinear Equation.

Written in collaboration with Petri Juutinen and Peter Lindqvist.
SIAM Journal of Mathematical Analysis Vol. 33, No. 3, pp. 699-717 (2001).
View Artice:
pdf
A Free Boundary Problem for the Infinite-Laplace Equation.
Written in collaboration with Arshak Petrosyan and Henrik Shahgolian.
Calc. Var. Partial Differential Equations 3 (2002), 359--384.
View article:
ps
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.
Draft. Your comments are welcome.
View Article:
pdf
Fundamental Solution for the Q-Laplacian and sharp Moser-Trudinger inequality in Carnot groups.
Written in collaboration with Zoltan Balogh and Jeremy Tyson.
Journal of Functional Analysis 204 (2003), 35--49.
View Article:
pdf
Convex functions in the Heisenberg group.
Written in collaboration with Guozhen Lu and Bianca Stroffolini.
Calc. Var. Partial Differential Equations 19 (2004), 1--22.
View Article:
pdf
Convex functions on Carnot groups.
Written in collaboration with Petri Juutinen, Guozhen Lu and Bianca Stroffolini.
Rev. Mat. Iberoamericana 23 (2007), no. 1, 191-201.
View Article:
pdf
Subelliptic Cordes Estimates.
Written in collaboration with Andras Domokos.
Proceedings of the American Mathematical Society 133 (2005), 1047--1056.
View Article:
pdf
C^{1,\alpha}-regularity for p-harmonic functions in the Heisenberg group for p near 2.
Written in collaboration with Andras Domokos.
In "The p-Harmonic Equation and Recent Advances in Analysis", ed. P. Poggi-Corradini, Contemporary Mathematics 370, American Mathematical Society, 2005.
View Article:
pdf
The Maximum Priniciple for Vector Fields.
Written in collaboration with Frank Beatrous and Thomas Bieske.
In "The p-Harmonic Equation and Recent Advances in Analysis", ed. P. Poggi-Corradini, Contemporary Mathematics 370, American Mathematical Society, 2005.
View Article:
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.
View Article:
pdf
Quasilinear Elliptic Equations in the Heisenberg group.
Written in collaboration with Giuseppe Mingione.
To appear in Mathematische Annalen.
View Article:
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
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.
View Article:
pdf
Steklov Eigenvalues for the infinity Laplacian.
Written in collaboration with J. Garcia-Azorero, I. Peral, and J. Rossi.
Rendiconti Lincei - Matematica e Applicazione 17 (3) (2006), 199-210.
View Article:
pdf
Divergence Forms of the Infinity-Laplacian.
Written in collaboration with L. D'Onofrio, F. Giannetti, T. Iwaniec, and T. Radice.
Publicationes Mathematiques 50 (1) (2006), 229-248.
View Article:
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.
View Article:
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.
View Article:
pdf
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.
View Article:
pdf

The Quasiworld

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

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.

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.

Jyväskylä Summer School, August 2005.

The Harnack Inequality for infinite-harmonic functions

Quasiregular Mappings from the Multilinear Point of View.

Regularity Theory and Traces for A-harmonic Functions

Mappings with Integrable Dilatation in Higher Dimensions

An extension of Reshetnyak's Theorem

Note on infinite-superharmonic functions

The infinite-Eigenvalue Problem

Traces of Monotone Functions on Weighted Sobolev Classes

Sobolev versus Hölder Local Minimizers and Global Multiplicity for some Quasilinear Elliptic Equations

Superharmonicity of Nonlinear Ground States

A Version of the Hopf-Lax formula in the Heisenberg Group.

Viscosity Solutions of the p-Laplace equation.

On the Equivalence of Viscosity Solutions and Weak Solutions for a Quasilinear Equation.

A Free Boundary Problem for the Infinite-Laplace Equation.

Rearrangements in Carnot Groups.

Fundamental Solution for the Q-Laplacian and sharp Moser-Trudinger inequality in Carnot groups.

Convex functions in the Heisenberg group.

Convex functions on Carnot groups.

Subelliptic Cordes Estimates.

C^{1,\alpha}-regularity for p-harmonic functions in the Heisenberg group for p near 2.

The Maximum Priniciple for Vector Fields.

p-Harmonic Measure is not Subadditive.

Quasilinear Elliptic Equations in the Heisenberg group.

Subelliptic Cordes Estimates in the Grushin Plane.

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

Steklov Eigenvalues for the infinity Laplacian.

Divergence Forms of the Infinity-Laplacian.

Note on a Remarkable Superposition for a Nonlinear Equation.

Viscosity Supersolutions of the Evolutionary p-Laplace Equation.

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