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Linear Holomorphic Partial Differential Equations and Classical Potential Theory
About this Title
Dmitry Khavinson, University of South Florida, Tampa, FL and Erik Lundberg, Florida Atlantic University, Boca Raton, FL
Publication: Mathematical Surveys and Monographs
Publication Year:
2018; Volume 232
ISBNs: 978-1-4704-3780-0 (print); 978-1-4704-4766-3 (online)
DOI: https://doi.org/10.1090/surv/232
MathSciNet review: MR3821527
MSC: Primary 35-02; Secondary 30B40, 31B20, 32A05, 35-01, 35A10, 35A20
Table of Contents
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Front/Back Matter
Chapters
- Introduction: Some motivating questions
- The Cauchy-Kovalevskaya theorem with estimates
- Remarks on the Cauchy-Kovalevskaya theorem
- Zernerâs theorem
- The method of globalizing families
- Holmgrenâs uniqueness theorem
- The continuity method of F. John
- The Bony-Schapira theorem
- Applications of the Bony-Schapira theorem: Part I - Vekua hulls
- Applications of the Bony-Schapira theorem: Part II - SzegĆâs theorem revisited
- The reflection principle
- The reflection principle (continued)
- Cauchy problems and the Schwarz potential conjecture
- The Schwarz potential conjecture for spheres
- Potential theory on ellipsoids: Part I - The mean value property
- Potential theory on ellipsoids: Part II - There is no gravity in the cavity
- Potential theory on ellipsoids: Part III - The Dirichlet problem
- Singularities encountered by the analytic continuation of solutions to the Dirichlet problem
- An introduction to J. Lerayâs principle on propagation of singularities through $\mathbb {C}^n$
- Global propagation of singularities in $\mathbb {C}^n$
- Quadrature domains and Laplacian growth
- Other varieties of quadrature domains
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