# Linear Holomorphic Partial Differential Equations and Classical Potential Theory

@article{Khavinson2018LinearHP, title={Linear Holomorphic Partial Differential Equations and Classical Potential Theory}, author={Dmitry Khavinson and Erik Lundberg}, journal={Mathematical Surveys and Monographs}, year={2018} }

## 34 Citations

### Point source equilibrium problems with connections to weighted quadrature domains

- MathematicsIndagationes Mathematicae
- 2022

### Inradius of random lemniscates

- Mathematics
- 2023

A BSTRACT . A classically studied geometric property associated to a complex polynomial p is the inradius (the radius of the largest inscribed disk) of its (ﬁlled) lemniscate Λ := { z ∈ C : | p ( z )…

### On generalized Fermat Diophantine functional and partial differential equations in C2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \be

- Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
- 2022

### Fischer decompositions for entire functions and the Dirichlet problem for parabolas

- Materials ScienceAnalysis and Mathematical Physics
- 2022

Let P2k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}…

### Bitensorial formulation of the singularity method for Stokes flows

- MathematicsMathematics in Engineering
- 2022

This paper develops the bitensorial formulation of the system of singularities associated with unbounded and bounded Stokes flows. The motivation for this extension is that Stokesian singularities…

### Harold Seymour Shapiro 1928–2021; Life in mathematics, in memoriam

- ArtAnalysis and Mathematical Physics
- 2022

This is a (very) personal outlook on the life and mathematical achievements of Harold S. Shapiro, who has passed away in March of 2021, a few days short of his 93rd birthday. It is based on the…

### Holomorphic solutions of soliton equations

- MathematicsTransactions of the Moscow Mathematical Society
- 2022

We present a holomorphic version of the inverse scattering method for soliton equations of parabolic type in two-dimensional space-time. It enables one to construct examples of solutions holomorphic…

### Extension theorems for harmonic functions which vanish on a subset of a cylindrical surface

- MathematicsJournal of Mathematical Analysis and Applications
- 2022

### Probabilistic bounds on best rank-one approximation ratio

- Mathematics, Computer Science
- 2022

We provide new upper and lower bounds on the minimum possible ratio of the spectral and Frobenius norms of a (partially) symmetric tensor. In the particular case of general tensors our result…

### Harmonic extension through conical surfaces

- MathematicsMathematische Annalen
- 2022

This paper establishes extension results for harmonic functions which vanish on a conical surface. These are based on a detailed analysis of expansions for the Green function of an infinite cone.

## References

### A theorem of nehari revisited

- Mathematics
- 1988

A well-known theorem of Z. Nehari shows how one can locate the singular points of a function f(z) given by where p n(z) is the Legendre polynomial of degree n, by relating them to the singular points…