Ebook: Partial Differential Equations with Minimal Smoothness and Applications

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.

---

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.

---

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.
Content:
Front Matter....Pages i-xiv
Weakly Elliptic Systems with Obstacle Constraints Part I — A 2 ? 2 Model Problem....Pages 1-14
Some Remarks on Widder’s Theorem and Uniqueness of Isolated Singularities for Parabolic Equations....Pages 15-23
Generalized Derivatives....Pages 25-32
On Null Sets of P-Harmonic Measures....Pages 33-36
Lifetime and Heat Kernel Estimates in Non-Smooth Domains....Pages 37-48
On the Poisson Kernel for Nondivergence Elliptic Equations with Continuous Coefficients....Pages 49-88
Some Questions Concerning Harmonic Measure....Pages 89-97
The Trace of the Heat Kernel in Domains with Nonsmooth Boundaries....Pages 99-104
A Note on L p Estimates for Parabolic Systems in Lipschitz Cylinders....Pages 105-109
Intrinsic Ultracontractivity and Probability....Pages 111-114
Uniqueness in the Dirichlet Problem for Time Independent Elliptic Operators....Pages 115-127
The Spectral Radius of the Classical Layer Potentials on Convex Domains....Pages 129-137
Unique Continuation for Degenerate Elliptic Equations....Pages 139-148
Sharp Estimates for Harmonic Measure in Convex Domains....Pages 149-162
On the Positive Solutions of the Free-Boundary Problem for Emden-Fowler Type Equations....Pages 163-172
Absolute Continuity of Parabolic Measure....Pages 173-188
Some Inequalities for the Density of the Area Integral....Pages 189-198
Restriction Theorems and the Schr?dinger Multiplier on the Torus....Pages 199-211
Numerical Analysis on Non-Smooth Problems: Some Examples....Pages 213-220

---

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.
Content:
Front Matter....Pages i-xiv
Weakly Elliptic Systems with Obstacle Constraints Part I — A 2 ? 2 Model Problem....Pages 1-14
Some Remarks on Widder’s Theorem and Uniqueness of Isolated Singularities for Parabolic Equations....Pages 15-23
Generalized Derivatives....Pages 25-32
On Null Sets of P-Harmonic Measures....Pages 33-36
Lifetime and Heat Kernel Estimates in Non-Smooth Domains....Pages 37-48
On the Poisson Kernel for Nondivergence Elliptic Equations with Continuous Coefficients....Pages 49-88
Some Questions Concerning Harmonic Measure....Pages 89-97
The Trace of the Heat Kernel in Domains with Nonsmooth Boundaries....Pages 99-104
A Note on L p Estimates for Parabolic Systems in Lipschitz Cylinders....Pages 105-109
Intrinsic Ultracontractivity and Probability....Pages 111-114
Uniqueness in the Dirichlet Problem for Time Independent Elliptic Operators....Pages 115-127
The Spectral Radius of the Classical Layer Potentials on Convex Domains....Pages 129-137
Unique Continuation for Degenerate Elliptic Equations....Pages 139-148
Sharp Estimates for Harmonic Measure in Convex Domains....Pages 149-162
On the Positive Solutions of the Free-Boundary Problem for Emden-Fowler Type Equations....Pages 163-172
Absolute Continuity of Parabolic Measure....Pages 173-188
Some Inequalities for the Density of the Area Integral....Pages 189-198
Restriction Theorems and the Schr?dinger Multiplier on the Torus....Pages 199-211
Numerical Analysis on Non-Smooth Problems: Some Examples....Pages 213-220
....