Potential Theory and Function Theory for Irregular Regions

Title: POTENTIAL THEORY AND FUNCTION THEORY FOR IRREGULAR REGIONS......Page 2
1969 Consultants Bureau......Page 3
FOREWORD......Page 5
CONTENTS......Page 7
PART 1: MOL TIV ARIA TE POTENTIAL THEORY AND THE SOLUTION OF BOUNDARY VALUE PROBLEMS FOR REGIONS WITH IRREGULAR BOUNDARIES......Page 8
INTRODUCTION......Page 10
§1. Definition and Certain Properties of a Solid Angle......Page 13
§ 2. Properties of Sets Satisfying Condition (A)......Page 17
§ 3. Properties of Sets Satisfying Condition (B)......Page 21
§ 4. Integral Equations of Boundary Value Problems......Page 24
§ 5. On the Continuity of the Simple-Layer Potential Generated by the Equation $\Phi - \lambda T^* \Phi =0$......Page 28
§ 6. Fredholm Radius of Operator T......Page 33
§7. Solvability and Uniqueness......Page 35
APPENDIX: ON THE APPROXIMATION OF A SOLID ANGLE......Page 39
LITERATURE CITED......Page 46
PART 2: ON THE SPACE OF FUNCTIONS WHOSE DERIVATIVES ARE MEASURES......Page 48
§ 1. Properties of the Set Perimeterand of Functions from $\beta V(\Omega)$......Page 50
§2. On the Continuation of Functionsfrom $\beta V(\Omega)$ onto the Whole Space......Page 52
§ 3. Certain Exact Constants for Convex Regions......Page 57
§4. The Rough Trace and Certain Integral Inequalities......Page 62
§ 5, The Trace of Functions from $\beta V(\Omega)$ on the Boundary......Page 67