Search results for " Bounded variation"
showing 4 items of 14 documents
MR3058477 Reviewed Ereú, Thomás; Sánchez, José L.; Merentes, Nelson; Wróbel, Małgorzata Uniformly continuous set-valued composition operators in the …
2011
In this paper it is established a property of a composition operator between spaces of functions of bounded variation in the sense of Schramm. Let X and Y be two real normed spaces, C a convex cone in X and I a closed bounded interval of the real line. Moreover let cc(Y) be the family of all non-empty closed convex and compact subsets of Y. The authors study the Nemytskij (composition) operator (HF)(t)=h(t,F(t)), where F: I \rightarrow C and h: I\times C \rightarrow cc(Y) is a given set-valued function. They show that if the Nemytskij operator $H$ is uniformly continuous and maps the space \Phi BV (I;C) of functions (from I to C) of bounded \Phi-variation in the sense of Schramm into the sp…
MR2789279 Aziz, Wadie; Leiva, Hugo; Merentes, Nelson; Rzepka, Beata A representation theorem for φ-bounded variation of functions in the sense of Rie…
2012
The authors consider the class $V_\varphi^R (I^b_a)$ of functions $f:I^b_a =[a_1,b_1]\times [a_2,b_2]\subset \mathbb{R}^2 \to \mathbb{R}$ with bounded $\varphi$-total variation in the sense of Riesz, where $\varphi: [0,+ \infty) \to [0,+ \infty)$ is nondecreasing and continuous with $\varphi(0)=0$ and $\varphi(t) \to +\infty$ as $t \to +\infty$. If we assume that $\varphi$ is also such that $\lim_{t \to +\infty}\frac{\varphi(t)}{t}= +\infty$, then we obtain the main result. Precisely, the authors give a characterization of function of two variables defined on a rectangle $I^b_a$ belonging to $V_\varphi^R (I^b_a)$. Clearly, this result is a generalization of the Riesz Lemma.
Measure differential inclusions: existence results and minimum problems
2020
AbstractWe focus on a very general problem in the theory of dynamic systems, namely that of studying measure differential inclusions with varying measures. The multifunction on the right hand side has compact non-necessarily convex values in a real Euclidean space and satisfies bounded variation hypotheses with respect to the Pompeiu excess (and not to the Hausdorff-Pompeiu distance, as usually in literature). This is possible due to the use of interesting selection principles for excess bounded variation set-valued mappings. Conditions for the minimization of a generic functional with respect to a family of measures generated by equiregulated left-continuous, nondecreasing functions and to…
Dimension reduction for $-Delta_1$
2012
A 3D-2D dimension reduction for $-\Delta_1$ is obtained. A power law approximation from $-\Delta_p$ as $p \to 1$ in terms of $\Gamma$- convergence, duality and asymptotics for least gradient functions has also been provided.