Absolutely Continuous Functions of Rado, Reichelderfer, and Malý

Absolutely continuous representatives on curves for Sobolev functions

We consider a class of Lipschitz vector fields S :Ω →Rn whose values lie in a suitable cone and we show that the trajectories of the system x′ = S(x) admit a parametrization that is invertible and Lipschitz with its inverse. As a consequence, every v in W1,1(Ω) admits a representative that is absolutely continuous on almost every trajectory of x′ = S(x). If S is an arbritrary Lipschitz field th...

Absolutely Continuous Functions with Values in Metric Spaces

(see e.g. [1, Lemma 1.1]), we could without any loss of generality work with Banach spaces only. The main obstacle in dealing with metric spaces (or arbitrary Banach spaces) is the absence of the Radon-Nikodým property and the resulting non-existence of derivatives. Thus, instead of the “usual” derivative, we have to employ the notion of a “metric derivative” (which was introduced by Kirchheim ...

On Absolutely Continuous Transformations

Non-absolutely Continuous Foliations

We consider a partially hyperbolic diffeomorphism of a compact smooth manifold preserving a smooth measure. Assuming that the central distribution is integrable to a foliation with compact smooth leaves we show that this foliation fails to have the absolute continuity property provided that the sum of Lyapunov exponents in the central direction is not zero on a set of positive measure. We also ...

existence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types

بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی ‎‏بیان شد‎‎‏ه اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...