scholarly journals Coepi-analysis of lower semicontinuity property of vector-valued mappings

2021 ◽  
Vol 18 ◽  
pp. 110
Author(s):  
A.V. Dovzhenko ◽  
P.I. Kogut
Keyword(s):  
Lower Semicontinuity ◽  
Lower Semicontinuous ◽  
Topological Properties ◽  
Variational Representation ◽  
Semicontinuity Property ◽  
Vector Valued

Topological properties of coepigraphs of vector-valued mappings are investigated. Lower semicontinuous regularization of such mappings and its variational representation are received with the help of coepigraphs.

scholarly journals Equivalence of viscosity and weak solutions for a p-parabolic equation

2021 ◽  
Author(s):  
Jarkko Siltakoski
Keyword(s):  
Parabolic Equation ◽  
Weak Solutions ◽  
Lower Semicontinuity ◽  
Lower Semicontinuous ◽  
Relationship Of ◽  
The Relationship

AbstractWe study the relationship of viscosity and weak solutions to the equation $$\begin{aligned} \smash {\partial _{t}u-\varDelta _{p}u=f(Du)}, \end{aligned}$$ ∂ t u - Δ p u = f ( D u ) , where $$p>1$$ p > 1 and $$f\in C({\mathbb {R}}^{N})$$ f ∈ C ( R N ) satisfies suitable assumptions. Our main result is that bounded viscosity supersolutions coincide with bounded lower semicontinuous weak supersolutions. Moreover, we prove the lower semicontinuity of weak supersolutions when $$p\ge 2$$ p ≥ 2 .

Lower semicontinuity of mass under C0{C^{0}} convergence and Huisken’s isoperimetric mass

2019 ◽  
Vol 2019 (756) ◽  
pp. 227-257 ◽  
Author(s):  
Jeffrey L. Jauregui ◽  
Dan A. Lee
Keyword(s):  
Scalar Curvature ◽  
Lower Semicontinuity ◽  
Mean Curvature ◽  
Total Mass ◽  
Mean Curvature Flow ◽  
Lower Semicontinuous ◽  
Curvature Flow ◽  
Three Dimensions ◽  
Asymptotically Flat ◽  
Limit Space

AbstractGiven a sequence of asymptotically flat 3-manifolds of nonnegative scalar curvature with outermost minimal boundary, converging in the pointed {C^{0}} Cheeger–Gromov sense to an asymptotically flat limit space, we show that the total mass of the limit is bounded above by the liminf of the total masses of the sequence. In other words, total mass is lower semicontinuous under such convergence. In order to prove this, we use Huisken’s isoperimetric mass concept, together with a modified weak mean curvature flow argument. We include a brief discussion of Huisken’s work before explaining our extension of that work. The results are all specific to three dimensions.

scholarly journals Some Vector FK Sequence Spaces Generated by Modulus Function

2020 ◽  
Vol 2 (2) ◽  
pp. 69-74
Author(s):  
E. Herawati ◽  
N. Irsyad ◽  
E. Rosmaini
Keyword(s):  
Sequence Spaces ◽  
Modulus Function ◽  
Topological Properties ◽  
Vector Valued

In this paper, some vector valued sequence spaces and using modulus function are presented. Furthermore, we examined some topological properties of these sequence spaces equipped with a paranorm.

scholarly journals Some New Lacunary Strong Convergent Vector-Valued Sequence Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
M. Mursaleen ◽  
A. Alotaibi ◽  
Sunil K. Sharma
Keyword(s):  
Orlicz Function ◽  
Sequence Spaces ◽  
Complex Numbers ◽  
Infinite Matrix ◽  
Topological Properties ◽  
Inclusion Relations ◽  
Vector Valued

We introduce some vector-valued sequence spaces defined by a Musielak-Orlicz function and the concepts of lacunary convergence and strong (A)-convergence, whereA=(aik)is an infinite matrix of complex numbers. We also make an effort to study some topological properties and some inclusion relations between these spaces.

scholarly journals The lower semicontinuity of the Frobenius splitting numbers

2010 ◽  
Vol 150 (1) ◽  
pp. 35-46 ◽  
Author(s):  
FLORIAN ENESCU ◽  
YONGWEI YAO
Keyword(s):  
Local Ring ◽  
Lower Semicontinuity ◽  
Lower Semicontinuous ◽  
Prime Characteristic ◽  
Frobenius Splitting ◽  
Mild Conditions ◽  
Splitting Numbers

AbstractWe show that, under mild conditions, the (normalized) Frobenius splitting numbers of a local ring of prime characteristic are lower semicontinuous.

scholarly journals ALMOST TRANSITIVITY IN $\mathcal{C}_0$ SPACES OF VECTOR-VALUED FUNCTIONS

2005 ◽  
Vol 48 (3) ◽  
pp. 513-529 ◽  
Author(s):  
Antonio Aizpuru ◽  
Fernando Rambla
Keyword(s):  
The Other ◽  
Dimension Theory ◽  
Topological Properties ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Stone Property

AbstractBy means of $M$-structure and dimension theory, we generalize some known results and obtain some new ones on almost transitivity in $\mathcal{C}_0(L,X)$. For instance, if $X$ has the strong Banach–Stone property, then almost transitivity of $\mathcal{C}_0(L,X)$ is divided into two weaker properties, one of them depending only on topological properties of $L$ and the other being closely related to the covering dimensions of $L$ and $X$. This leads to some non-trivial examples of almost transitive $\mathcal{C}_0(L,X)$ spaces.

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