There is a fundamental relation between the capacity of a set and energy integrals of probability measures supported on that set. If the capacity is small the energy integral will be large; in particular sets of capacity zero cannot support probability measures of …nite energy. Here we develop similar ideas relating capacity to Carleson measures. We show that if a set has small capacity then an...

We construct and analyze the backward Euler method for one nonlinear one-dimensional parabolic equation with nonlocal boundary condition. The main objective of this article is to investigate stability convergence difference scheme in maximum norm. For purpose, we use M-matrices theory. describe some new approach estimation error solution majorant it. Some conclusions discussion our are presented.

The paper is devoted to the study of mappings satisfying inverse Poletsky inequality. We local behavior these mappings. are most interested in case when corresponding majorant integrable on some set spheres positive linear measure. Our main result a logarithmic Hölder continuity such at inner points. As corollary, we have established existence continuous ACL-solution Beltrami equation, which co...

Using inequalities for a certain function appearing in the half-linear version of Picone’s identity, we show that oscillatory properties of the half-linear second-order differential equation (r(t)Φ(x′))′ + c(t)Φ(x) = 0, Φ(x) = |x|p−2x, p > 1, can be investigated via oscillatory properties of a certain associated second-order linear differential equation. This linear equation plays the role of a...