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Multiplicity and Stability of the Pohozaev Obstruction for Hardy-Schrödinger Equations with Boundary Singularity
 
Nassif Ghoussoub University of British Columbia, Vancouver, Canada
Saikat Mazumdar Indian Institute of Technology Bombay, Mumbai, India
Frédéric Robert Université de Lorraine, Nancy, France
Softcover ISBN:  978-1-4704-6119-5
Product Code:  MEMO/285/1415
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
eBook ISBN:  978-1-4704-7485-0
Product Code:  MEMO/285/1415.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-6119-5
eBook: ISBN:  978-1-4704-7485-0
Product Code:  MEMO/285/1415.B
List Price: $170.00 $127.50
MAA Member Price: $153.00 $114.75
AMS Member Price: $136.00 $102.00
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Multiplicity and Stability of the Pohozaev Obstruction for Hardy-Schrödinger Equations with Boundary Singularity
Nassif Ghoussoub University of British Columbia, Vancouver, Canada
Saikat Mazumdar Indian Institute of Technology Bombay, Mumbai, India
Frédéric Robert Université de Lorraine, Nancy, France
Softcover ISBN:  978-1-4704-6119-5
Product Code:  MEMO/285/1415
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
eBook ISBN:  978-1-4704-7485-0
Product Code:  MEMO/285/1415.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Softcover ISBN:  978-1-4704-6119-5
eBook ISBN:  978-1-4704-7485-0
Product Code:  MEMO/285/1415.B
List Price: $170.00 $127.50
MAA Member Price: $153.00 $114.75
AMS Member Price: $136.00 $102.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2852023; 126 pp
    MSC: Primary 35

    View the abstract.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Setting up the blow-up
    • 3. Scaling Lemmas
    • 4. Construction and exhaustion of the blow-up scales
    • 5. Strong pointwise estimates
    • 6. Sharp blow-up rates and the proof of Compactness
    • 7. Estimates on the localized Pohozaev identity
    • 8. Estimates of the $L^{2^\star (s)}$ and $L^2-$terms in the localized Pohozaev identity
    • 9. Estimate of the curvature term in the Pohozaev identity when $\beta _+(\gamma )-\beta _-(\gamma )>1$
    • 10. Proof of the sharp blow-up rates
    • 11. Proof of multiplicity
    • A. The Pohozaev identity
    • B. A continuity property of the first eigenvalue of Schrödinger operators
    • C. Regularity and the Hardy-Schrödinger operator on $\mathbb {R}^{n}_{-}$
    • D. Green’s function for the Hardy-Schrödinger operator with boundary singularity on a bounded domain
    • E. Green’s function for the Hardy-Schrödinger operator on $\mathbb {R}_{-}^n$
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 2852023; 126 pp
MSC: Primary 35

View the abstract.

  • Chapters
  • 1. Introduction
  • 2. Setting up the blow-up
  • 3. Scaling Lemmas
  • 4. Construction and exhaustion of the blow-up scales
  • 5. Strong pointwise estimates
  • 6. Sharp blow-up rates and the proof of Compactness
  • 7. Estimates on the localized Pohozaev identity
  • 8. Estimates of the $L^{2^\star (s)}$ and $L^2-$terms in the localized Pohozaev identity
  • 9. Estimate of the curvature term in the Pohozaev identity when $\beta _+(\gamma )-\beta _-(\gamma )>1$
  • 10. Proof of the sharp blow-up rates
  • 11. Proof of multiplicity
  • A. The Pohozaev identity
  • B. A continuity property of the first eigenvalue of Schrödinger operators
  • C. Regularity and the Hardy-Schrödinger operator on $\mathbb {R}^{n}_{-}$
  • D. Green’s function for the Hardy-Schrödinger operator with boundary singularity on a bounded domain
  • E. Green’s function for the Hardy-Schrödinger operator on $\mathbb {R}_{-}^n$
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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