Dahlberg B., Fefferman R., Kenig C., Fabes E., Jerison D., Pipher J. (eds.) Partial Differential Equations with Minimal Smoothness and Applications

Springer, 1992. — 226 p.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.Front Matter
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 L p 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.