eBook ISBN:  9780821887509 
Product Code:  MEMO/217/1019.E 
List Price:  $60.00 
MAA Member Price:  $54.00 
AMS Member Price:  $36.00 
eBook ISBN:  9780821887509 
Product Code:  MEMO/217/1019.E 
List Price:  $60.00 
MAA Member Price:  $54.00 
AMS Member Price:  $36.00 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 217; 2012; 77 ppMSC: Primary 35; Secondary 30
This paper deals with elliptic equations in the plane with degeneracies. The equations are generated by a complex vector field that is elliptic everywhere except along a simple closed curve. Kernels for these equations are constructed. Properties of solutions, in a neighborhood of the degeneracy curve, are obtained through integral and series representations. An application to a second order elliptic equation with a punctual singularity is given.

Table of Contents

Chapters

Introduction

1. Preliminaries

2. Basic Solutions

3. Example

4. Asymptotic behavior of the basic solutions of $\mathcal {L}$

5. The kernels

6. The homogeneous equation $\mathcal {L} u=0$

7. The nonhomogeneous equation $\mathcal {L} u=F$

8. The semilinear equation

9. The second order equation: Reduction

10. The homogeneous equation $Pu=0$

11. The nonhomogeneous equation $Pu=F$

12. Normalization of a Class of Second Order Equations with a Singularity


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This paper deals with elliptic equations in the plane with degeneracies. The equations are generated by a complex vector field that is elliptic everywhere except along a simple closed curve. Kernels for these equations are constructed. Properties of solutions, in a neighborhood of the degeneracy curve, are obtained through integral and series representations. An application to a second order elliptic equation with a punctual singularity is given.

Chapters

Introduction

1. Preliminaries

2. Basic Solutions

3. Example

4. Asymptotic behavior of the basic solutions of $\mathcal {L}$

5. The kernels

6. The homogeneous equation $\mathcal {L} u=0$

7. The nonhomogeneous equation $\mathcal {L} u=F$

8. The semilinear equation

9. The second order equation: Reduction

10. The homogeneous equation $Pu=0$

11. The nonhomogeneous equation $Pu=F$

12. Normalization of a Class of Second Order Equations with a Singularity