EXISTENCE, UNIQUENESS AND OPTIMAL REGULARITY RESULTS FOR VERY WEAK SOLUTIONS TO NONLINEAR ELLIPTIC SYSTEMS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10332628" target="_blank" >RIV/00216208:11320/16:10332628 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.2140/apde.2016.9.1115" target="_blank" >http://dx.doi.org/10.2140/apde.2016.9.1115</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.2140/apde.2016.9.1115" target="_blank" >10.2140/apde.2016.9.1115</a>

Jazyk výsledku

angličtina

Název v původním jazyce

EXISTENCE, UNIQUENESS AND OPTIMAL REGULARITY RESULTS FOR VERY WEAK SOLUTIONS TO NONLINEAR ELLIPTIC SYSTEMS

Popis výsledku v původním jazyce

We establish existence, uniqueness and optimal regularity results for very weak solutions to certain nonlinear elliptic boundary value problems. We introduce structural asymptotic assumptions of Uhlenbeck type on the nonlinearity, which are sufficient and in many cases also necessary for building such a theory. We provide a unified approach that leads qualitatively to the same theory as the one available for linear elliptic problems with continuous coefficients, e.g., the Poisson equation. The result is based on several novel tools that are of independent interest: local and global estimates for (non) linear elliptic systems in weighted Lebesgue spaces with Muckenhoupt weights, a generalization of the celebrated div-curl lemma for identification of a weak limit in border line spaces and the introduction of a Lipschitz approximation that is stable in weighted Sobolev spaces.

Název v anglickém jazyce

EXISTENCE, UNIQUENESS AND OPTIMAL REGULARITY RESULTS FOR VERY WEAK SOLUTIONS TO NONLINEAR ELLIPTIC SYSTEMS

Popis výsledku anglicky

We establish existence, uniqueness and optimal regularity results for very weak solutions to certain nonlinear elliptic boundary value problems. We introduce structural asymptotic assumptions of Uhlenbeck type on the nonlinearity, which are sufficient and in many cases also necessary for building such a theory. We provide a unified approach that leads qualitatively to the same theory as the one available for linear elliptic problems with continuous coefficients, e.g., the Poisson equation. The result is based on several novel tools that are of independent interest: local and global estimates for (non) linear elliptic systems in weighted Lebesgue spaces with Muckenhoupt weights, a generalization of the celebrated div-curl lemma for identification of a weak limit in border line spaces and the introduction of a Lipschitz approximation that is stable in weighted Sobolev spaces.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

—

Projekt

<a href="/cs/project/LL1202" target="_blank" >LL1202: Materiály s implicitními konstitutivními vztahy: Od teorie přes redukci modelů k efektivním numerickým metodám</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

Analysis and PDE [online]

ISSN

1948-206X

e-ISSN

—

Svazek periodika

9

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

37

Strana od-do

1115-1151

Kód UT WoS článku

000381769200004

EID výsledku v databázi Scopus

2-s2.0-84982078830