The P-harmonic Equation and Recent Advances in Analysis

by POGGI-CORRADINI, PIETRO; Prairie Analysis Seminar 2003 Kansas Sta

• ISBN13: 9780821836101
• ISBN10: 0821836102
• Format: Paperback
• Copyright: 2005-03-01
• Publisher: Amer Mathematical Society

Summary

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.

Table of Contents

Preface	vii
Program	ix
The maximum principle for vector fields	1	(10)
Frank H. Beatrous
Thomas J. Bieske
Juan J. Manfredi
A partial classification of the blowups of the singularities in a composite membrane problem	11	(6)
Ivan Blank
C1α-regularity for p-harmonic functions in the Heisenberg group for p near 2	17	(8)
Andras Domokos
Juan J. Manfredi
Notes on p-harmonic analysis	25	(26)
Luigi D'Onofrio
Tadeusz Iwaniec
A condition sufficient for the partial regularity of minimizers in two-dimensional nonlinear elasticity	51	(48)
M. Foss
Dynamics on bounded domains	99	(20)
Chiara Frosini
On the rate of tangential convergence of functions from Hardy spaces, 0 < p < 1	119	(14)
Kathryn E. Hare
Alexander M. Stokolos
Counter-examples of regularity in variable exponent Sobolev spaces	133	(12)
Peter A. Hasto
Quasiregular gradient mappings and strong solutions of elliptic equations	145	(14)
Leonid V. Kovalev
David Opela
Harmonic, monogenic and hypermonogenic functions on some conformally flat manifolds in Rn arising from special arithmetic groups of the Vahlen group	159	(16)
R. S. Krausshar
Yuying Qiao
John Ryan
On symmetry and uniform rectifiability arising from some overdetermined elliptic and parabolic boundary conditions	175	(14)
John L. Lewis
Recent progress on the Monge-Ampere equation	189	(10)
Liliana Forzani
Diego Maldonado
Mappings of finite distortion: Future directions and problems	199	(10)
Jani Onninen
Riemann-Hurwitz formula and Morse theory	209
Malgorzata Stawiska