Partial Differential Equations with Minimal Smoothness and Applications

ISBN-13: 9781461277125 / Angielski / Miękka / 2011 / 220 str.

B. Dahlberg; Eugene Fabes; R. Fefferman

Opis

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.

Spis treści

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.