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The \(p\)-Harmonic Equation and Recent Advances in Analysis
Edited by: Pietro Poggi-Corradini, Kansas State University, Manhattan, KS
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Contemporary Mathematics
2005; 211 pp; softcover
Volume: 370
ISBN-10: 0-8218-3610-2
ISBN-13: 978-0-8218-3610-1
List Price: US$65
Member Price: US$52
Order Code: CONM/370
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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

  • F. H. Beatrous, T. J. Bieske, and J. J. Manfredi -- The maximum principle for vector fields
  • I. Blank -- A partial classification of the blowups of the singularities in a composite membrane problem
  • A. Domokos and J. J. Manfredi -- \(C^{1,\alpha}\)-regularity for \(p\)-harmonic functions in the Heisenberg group for \(p\) near 2
  • L. D'Onofrio and T. Iwaniec -- Notes on \(p\)-harmonic analysis
  • M. Foss -- A condition sufficient for the partial regularity of minimizers in two-dimensional nonlinear elasticity
  • C. Frosini -- Dynamics on bounded domains
  • K. E. Hare and A. M. Stokolos -- On the rate of tangential convergence of functions from Hardy spaces, \(0<p<1\)
  • P. A. Hästö -- Counter-examples of regularity in variable exponent Sobolev spaces
  • L. V. Kovalev and D. Opěla -- Quasiregular gradient mappings and strong solutions of elliptic equations
  • R. S. Krausshar, Y. Qiao, and J. Ryan -- Harmonic, monogenic and hypermonogenic functions on some conformally flat manifolds in \(R^n\) arising from special arithmetic groups of the Vahlen group
  • J. L. Lewis -- On symmetry and uniform rectifiability arising from some overdetermined elliptic and parabolic boundary conditions
  • L. Forzani and D. Maldonado -- Recent progress on the Monge-Ampère equation
  • J. Onninen -- Mappings of finite distortion: Future directions and problems
  • M. Stawiska -- Riemann-Hurwitz formula and Morse theory
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