• Corpus ID: 117548743

Selected works of Eberhard Hopf with commentaries

  title={Selected works of Eberhard Hopf with commentaries},
  author={Eberhard Hopf and Cathleen Synge Morawetz and James Serrin and Iakov Grigorevich Sinai},
Part I: Elementare Bemerkungen uber die Losungen partieller Differentialgleichungen zweiter Ordnung vom elliptischen Typus by E. Hopf Commentary by J. B. Serrin A remark on linear elliptic differential equations of second order by E. Hopf Commentary by J. B. Serrin Zum analytischen Charakter der Losungen regularer zweidimensionaler Variationsprobleme by E. Hopf Commentary by H. Weinberger Uber eine Klasse singularer Integralgleichungen by N. Wiener and E. Hopf Commentary by H. Widom Uber den… 

On the regularity of domains satisfying a uniform hour–glass condition and a sharp version of the Hopf–Oleinik boundary point principle

We prove that an open, proper, nonempty subset of ${\mathbb{R}}^n$ is a locally Lyapunov domain if and only if it satisfies a uniform hour-glass condition. The limiting cases are as follows:


It is well known that the concept of a generalized solution from the Sobolev space W 12 of the Dirichlet problem for a second order elliptic equation is not a generalization of the classical solution

Hopf bifurcation for non-densely defined Cauchy problems

In this paper, we establish a Hopf bifurcation theorem for abstract Cauchy problems in which the linear operator is not densely defined and is not a Hille–Yosida operator. The theorem is proved using

Dolbeault cohomology for almost complex manifolds

This paper extends Dolbeault cohomology and its surrounding theory to arbitrary almost complex manifolds. We define a spectral sequence converging to ordinary cohomology, whose first page is the

Maximum Principles for vectorial approximate minimizers of nonconvex functionals

We establish Maximum Principles which apply to vectorial approximate minimizers of the general integral functional of Calculus of Variations. Our main result is a version of the Convex Hull Property.

Eberhard Hopf between Germany and the US

The curriculum vitae of Eberhard Hopf was not unique, but very unusual: He was one of the very few German scientists who moved from the US to Germany in 1936, and this though he had a secure position

A Hopf's lemma and the boundary regularity for the fractional p-Laplacian

We begin the paper with a Hopf's lemma for a fractional p-Laplacian problem on a half-space. Specifically speaking, we show that the derivative of the solution along the outward normal vector is

Linear scale-spaces in image processing: drift-diffusion and connections to mathematical morphology

This work develops a complete scale-space theory for the linear osmosis filtering and introduces the novel Cramér-Fourier transform, which shows that a Fourier-based transform is much more natural in an image processing context.

Large deviations principle for stationary solutions of stochastic differential equations with multiplicative noise

We study the large deviations principle (LDP) for stationary solutions of a class of stochastic differential equations (SDE) in infinite time intervals by the weak convergence approach, and then