**Contemporary Mathematics**

Volume: 370;
2005;
211 pp;
Softcover

MSC: Primary 30; 31; 32; 35; 46; 47;

Print ISBN: 978-0-8218-3610-1

Product Code: CONM/370

List Price: $69.00

AMS Member Price: $55.20

MAA Member Price: $62.10

**Electronic ISBN: 978-0-8218-7960-3
Product Code: CONM/370.E**

List Price: $69.00

AMS Member Price: $55.20

MAA Member Price: $62.10

# The \(p\)-Harmonic Equation and Recent Advances in Analysis

Share this page *Edited by *
*Pietro Poggi-Corradini*

Comprised of papers from the IIIrd Prairie Analysis Seminar held at Kansas
State University, this book reflects the many directions of current research in
harmonic analysis and partial differential equations. Included is the work of
the distinguished main speaker, Tadeusz Iwaniec, his invited guests John Lewis
and Juan Manfredi, and many other leading researchers.

The main topic is the so-called p-harmonic equation, which is a family of
nonlinear partial differential equations generalizing the usual Laplace
equation. This study of p-harmonic equations touches upon
many areas of analysis with deep relations to functional analysis, potential
theory, and calculus of variations.

The material is suitable for graduate students and research mathematicians
interested in harmonic analysis and partial differential equations.

#### Readership

Graduate students and research mathematicians interested in harmonic analysis and partial differential equations.

# Table of Contents

## The $p$-Harmonic Equation and Recent Advances in Analysis

- Contents v6 free
- Preface vii8 free
- Program ix10 free
- The maximum principle for vector fields 112 free
- A partial classification of the blowups of the singularities in a composite membrane problem 1122
- C1,α-regularity for p-harmonic functions in the Heisenberg group for p near 2 1728
- Notes on p-harmonic analysis 2536
- A condition sufficient for the partial regularity of minimizers in two-dimensional nonlinear elasticity 5162
- Dynamics on bounded domains 99110
- On the rate of tangential convergence of functions from Hardy spaces, 0<p<1 119130
- Counter-examples of regularity in variable exponent Sobolev spaces 133144
- Quasiregular gradient mappings and strong solutions of elliptic equations 145156
- Harmonic, monogenic and hypermonogenic functions on some conformally flat manifolds in Rn arising from special arithmetic groups of the Vahlen group 159170
- On symmetry and uniform rectifiability arising from some overdetermined elliptic and parabolic boundary conditions 175186
- Recent progress on the Monge-Ampère equation 189200
- Mappings of finite distortion: Future directions and problems 199210
- Riemann-Hurwitz formula and Morse theory 209220