On grand and small Lebesgue and Sobolev spaces and some applications to PDEs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F18%3A00486954" target="_blank" >RIV/67985840:_____/18:00486954 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.7153/dea-2018-10-03" target="_blank" >http://dx.doi.org/10.7153/dea-2018-10-03</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.7153/dea-2018-10-03" target="_blank" >10.7153/dea-2018-10-03</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On grand and small Lebesgue and Sobolev spaces and some applications to PDEs

Popis výsledku v původním jazyce

This paper is essentially a survey on grand and small Lebesgue spaces, which arerearrangement-invariant Banach function spaces of interest not only from the point of view of Function Spaces theory, but also from the point of view of their applications: the corresponding Sobolev spaces are of interest, for instance, in the theory of PDEs. We discuss results of existence, uniqueness and regularity of certain Dirichlet problems, where the knowledge of these spaces plays a central role. The novelty of this paper relies in an unified treatment containing a number of equivalent quasinorms, all written making explicit the dependence of |omega|, in the discussion of the sharpness of Hölder’s inequality, and in the connection of the results in PDEs with some existing literature.

Název v anglickém jazyce

On grand and small Lebesgue and Sobolev spaces and some applications to PDEs

Popis výsledku anglicky

This paper is essentially a survey on grand and small Lebesgue spaces, which arerearrangement-invariant Banach function spaces of interest not only from the point of view of Function Spaces theory, but also from the point of view of their applications: the corresponding Sobolev spaces are of interest, for instance, in the theory of PDEs. We discuss results of existence, uniqueness and regularity of certain Dirichlet problems, where the knowledge of these spaces plays a central role. The novelty of this paper relies in an unified treatment containing a number of equivalent quasinorms, all written making explicit the dependence of |omega|, in the discussion of the sharpness of Hölder’s inequality, and in the connection of the results in PDEs with some existing literature.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA13-14743S" target="_blank" >GA13-14743S: Prostory funkcí, váhové nerovnosti a interpolace II</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2018

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Differential Equations & Applications

ISSN

1847-120X

e-ISSN

—

Svazek periodika

10

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

HR - Chorvatská republika

Počet stran výsledku

26

Strana od-do

21-46

Kód UT WoS článku

000427853100003

EID výsledku v databázi Scopus

—