Partial Differential Equations with Minimal Smoothness and Applications

Overview

In recent years there has been a great deal of activity in both the theoretical and applied aspects of partial differential equations, with emphasis on realistic engineering applications, which usually involve lack of smoothness. On March 21-25, 1990, the University of Chicago hosted a workshop that brought together approximately fortyfive experts in theoretical and applied aspects of these subjects. The workshop was a vehicle for summarizing the current status of research in these areas, and for defining new ...

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Overview

In recent years there has been a great deal of activity in both the theoretical and applied aspects of partial differential equations, with emphasis on realistic engineering applications, which usually involve lack of smoothness. On March 21-25, 1990, the University of Chicago hosted a workshop that brought together approximately fortyfive experts in theoretical and applied aspects of these subjects. The workshop was a vehicle for summarizing the current status of research in these areas, and for defining new directions for future progress - this volume contains articles from participants of the workshop.

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Editorial Reviews

Booknews
Summarizes the current research, and projects new trends, in the theoretical and applied aspects of partial differential equations, emphasizing their use in realistic engineering problems, which usually involve a lack of smoothness. The 19 papers are from a workshop in Chicago in March 1990. No index. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9781461277125
  • Publisher: Springer New York
  • Publication date: 7/31/2012
  • Series: IMA Volumes in Mathematics and its Applications Series , #42
  • Edition description: Softcover reprint of the original 1st ed. 1992
  • Edition number: 1
  • Pages: 220
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.51 (d)

Table of Contents

Weakly elliptic systems with obstacle constraints. Part I — a 2 × 2 model problem.- Some remarks on Widder’s theorem and uniqueness of isolated singularities for parabolic equations.- Generalized derivatives.- On null sets of P-harmonic measures.- Lifetime and heat kernel estimates in non-smooth domains.- On the Poisson kernel for nondivergence elliptic equations with continuous coefficients.- Some questions concerning harmonic measure.- The trace of the heat kernel in domains with nonsmooth boundaries.- A note on Lp estimates for parabolic systems in Lipschitz cylinders.- Intrinsic ultracontractivity and probability.- Uniqueness in the Dirichlet problem for time independent elliptic operators.- The spectral radius of the classical layer potentials on convex domains.- Unique continuation for degenerate elliptic equations.- Sharp estimates for harmonic measure in convex domains.- On the positive solutions of the free-boundary problem for Emden-Fowler type equations.- Absolute continuity of parabolic measure.- Some inequalities for the density of the area integral.- Restriction theorems and the Schrödinger multiplier on the torus.- Numerical analysis on non-smooth problems: Some examples.

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