Applications of Interpolation theory to the regularity of some quasilinear PDEs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F25%3A00619397" target="_blank" >RIV/67985840:_____/25:00619397 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.15673/pigc.v18i1.2865" target="_blank" >https://doi.org/10.15673/pigc.v18i1.2865</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.15673/pigc.v18i1.2865" target="_blank" >10.15673/pigc.v18i1.2865</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Applications of Interpolation theory to the regularity of some quasilinear PDEs

Popis výsledku v původním jazyce

We present some regularity results on the gradient of the weak or entropic-renormalized solution $u$ to the homogeneous Dirichlet problem for the quasilinear equations of the formnbegin{equation*}label{p-laplacian_eq} -div(|abla u|^{p-2} abla u)+V(x,u)=f, end{equation*} where $Omega$ is a bounded smooth domain of $mathbb R^n$, $V$ is a nonlinear potential and $f$ belongs to non-standard spaces like Lorentz-Zygmund spaces. nThe results, which have been exposed by the third author in a talk presented in AGMA 2024, the International Scientific Online Conference «Algebraic and geometric methods of analysis», May 27-30, 2024, Ukraine, constitute only a part of results proved in detail in a paper coauthored with I. Ahmed, A. Fiorenza, A. Gogatishvili, A. El Hamidi and J.M. Rakotoson.nMoreover, we collect some well-known and new results of the identication of some interpolation spaces and we enrich some contents with details.

Název v anglickém jazyce

Applications of Interpolation theory to the regularity of some quasilinear PDEs

Popis výsledku anglicky

We present some regularity results on the gradient of the weak or entropic-renormalized solution $u$ to the homogeneous Dirichlet problem for the quasilinear equations of the formnbegin{equation*}label{p-laplacian_eq} -div(|abla u|^{p-2} abla u)+V(x,u)=f, end{equation*} where $Omega$ is a bounded smooth domain of $mathbb R^n$, $V$ is a nonlinear potential and $f$ belongs to non-standard spaces like Lorentz-Zygmund spaces. nThe results, which have been exposed by the third author in a talk presented in AGMA 2024, the International Scientific Online Conference «Algebraic and geometric methods of analysis», May 27-30, 2024, Ukraine, constitute only a part of results proved in detail in a paper coauthored with I. Ahmed, A. Fiorenza, A. Gogatishvili, A. El Hamidi and J.M. Rakotoson.nMoreover, we collect some well-known and new results of the identication of some interpolation spaces and we enrich some contents with details.

Druh

J_SC - Článek v periodiku v databázi SCOPUS

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA23-04720S" target="_blank" >GA23-04720S: Jemné vlastnosti funkcí, operátorů a prostorů funkcí</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Proceedings of the International Geometry Center

ISSN

2072-9812

e-ISSN

2409-8906

Svazek periodika

18

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

UA - Ukrajina

Počet stran výsledku

34

Strana od-do

35-68

Kód UT WoS článku

—

EID výsledku v databázi Scopus

2-s2.0-105010060416