Results 91 to 100 of about 3,996 (166)

The regularity of the positive part of functions in $L^2(I; H^1(\Omega)) \cap H^1(I; H^1(\Omega)^*)$ with applications to parabolic equations

, 2016
Let $u\in L^2(I; H^1(\Omega))$ with $\partial_t u\in L^2(I; H^1(\Omega)^*)$ be given. Then we show by means of a counter-example that the positive part $u^+$ of $u$ has less regularity, in particular it holds $\partial_t u^+ \not\in L^1(I; H^1(\Omega)^*)$
Wachsmuth, Daniel
core   +1 more source

Dilation in function spaces with general weights [PDF]

arXiv, 2020
In this paper, we present more regularity conditions which ensure the boundedness of dilation operators on Besov and Triebel-Lizorkin spaces equiped with general weights.
arxiv  

Continuity properties for Riesz potentials of functions in Morrey spaces of variable exponent

, 2010
Our aim in this paper is to deal with continuity properties for Riesz potentials of functions in Morrey spaces of variable exponent. The modulus of continuity is determined by the structure of Morrey space.
Y. Mizuta, T. Shimomura
semanticscholar   +1 more source

Boundedness of generalized Riesz potentials of functions in Morrey spaces L^(1,φ;κ)(G) over non-doubling measure spaces

Mathematical Inequalities & Applications, 2019
Our aim in this paper is to deal with the boundedness of generalized Riesz potentials Iρ,μ ,τ f of functions in Morrey spaces L(1,φ;κ)(G) over non-doubling measure spaces, as an extension of [4, 6, 9, 12, 19].
Y. Sawano, T. Shimomura
semanticscholar   +1 more source

A remark on the history of Hardy inequalities in domains [PDF]

arXiv, 2004
This a very brief account of the main line of development of Hardy inequalities.
arxiv  

Extrapolation: Stories and Problems [PDF]

arXiv, 2020
We discuss some aspects of Extrapolation theory. The presentation includes many examples and open problems.
arxiv  

Existence and multiplicity of solutions for equations involving nonhomogeneous operators of p(x)-Laplace type in RN

, 2014
We are concerned with the following elliptic equations with variable exponents: −div(φ(x,∇u))+|u|p(x)−2u=λf(x,u) in RN, where the function φ(x,v) is of type |v|p(x)−2v with continuous function p:RN→(1,∞) and f:RN×R→R satisfies a Carathéodory condition ...
Seung Dae Lee, Kisoeb Park, Yun-Ho Kim
semanticscholar   +1 more source

Local one-sided maximal function on fractional Sobolev spaces

Mathematical Inequalities & Applications, 2019
In this article we study the boundedness of local one sided maximal operators on weighted fractional Sobolev Spaces. As a consequence we obtain a Lebesgue differentiation theorem for functions in fractional Sobolev spaces.
A. Ghosh, Kalachand Shuin
semanticscholar   +1 more source

A note on the Trace Theorem for domains which are locally subgraph of a Holder continuous function [PDF]

, 2013
The purpose of this note is to prove a version of the Trace Theorem for domains which are locally subgraph of a H\" older continuous function.
Muha, Boris
core  

Lp Hardy's identities and inequalities for Dunkl operators

Advanced Nonlinear Studies, 2022
The main purpose of this article is to establish the Lp{L}^{p} Hardy’s identities and inequalities for Dunkl operator on any finite balls and the entire space RN{{\mathbb{R}}}^{N}. We also prove Hardy’s identities and inequalities on certain domains with
Wang Jianxiong
doaj   +1 more source