Page 1 Next

Displaying 1 – 20 of 248

Showing per page

A 3G-Theorem for Jordan Domains in ℝ²

Lotfi Riahi (2004)

Colloquium Mathematicae

We prove a new 3G-Theorem for the Laplace Green function G on an arbitrary Jordan domain D in ℝ². This theorem extends the recent one proved on a Dini-smooth Jordan domain.

A Nevanlinna theorem for superharmonic functions on Dirichlet regular Greenian sets

Neil A. Watson (2005)

Mathematica Bohemica

A generalization of Nevanlinna’s First Fundamental Theorem to superharmonic functions on Green balls is proved. This enables us to generalize many other theorems, on the behaviour of mean values of superharmonic functions over Green spheres, on the Hausdorff measures of certain sets, on the Riesz measures of superharmonic functions, and on differences of positive superharmonic functions.

A remark on gradients of harmonic functions.

Wen Sheng Wang (1995)

Revista Matemática Iberoamericana

In any C1,s domain, there is nonzero harmonic function C1 continuous up to the boundary such that the function and its gradient on the boundary vanish on a set of positive measure.

A stability theorem for elliptic Harnack inequalities

Richard F. Bass (2013)

Journal of the European Mathematical Society

We prove a stability theorem for the elliptic Harnack inequality: if two weighted graphs are equivalent, then the elliptic Harnack inequality holds for harmonic functions with respect to one of the graphs if and only if it holds for harmonic functions with respect to the other graph. As part of the proof, we give a characterization of the elliptic Harnack inequality.

A Weak-Type Inequality for Orthogonal Submartingales and Subharmonic Functions

Adam Osękowski (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

Let X be a submartingale starting from 0, and Y be a semimartingale which is orthogonal and strongly differentially subordinate to X. The paper contains the proof of the sharp estimate ( s u p t 0 | Y t | 1 ) 3 . 375 . . . X . As an application, a related weak-type inequality for smooth functions on Euclidean domains is established.

Currently displaying 1 – 20 of 248

Page 1 Next