Non-linear Gagliardo-Nirenberg inequality involving a second-order elliptic operator in non-divergent form
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F60076658%3A12410%2F25%3A43910132" target="_blank" >RIV/60076658:12410/25:43910132 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/25:10513201
Result on the web
<a href="https://link.springer.com/article/10.1007/s00030-025-01124-9" target="_blank" >https://link.springer.com/article/10.1007/s00030-025-01124-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00030-025-01124-9" target="_blank" >10.1007/s00030-025-01124-9</a>
Alternative languages
Result language
angličtina
Original language name
Non-linear Gagliardo-Nirenberg inequality involving a second-order elliptic operator in non-divergent form
Original language description
We obtain the inequalities of the form integral Omega|del u(x)|2h(u(x))dx <= C integral Omega|Pu(x)||TH(u(x))|2h(u(x))dx+Theta,documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$int _{Omega }|nabla u(x)|<^>2h(u(x)),d xle Cint _{Omega } left( sqrt{ |P u(x)||{mathcal {T}}_{H}(u(x))|}right) <^>{2}h(u(x)),d x +Theta ,$$end{document}where Omega subset of Rndocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$Omega subset {textbf{R}<^>{n}}$$end{document} is a bounded Lipschitz domain, u is an element of Wloc2,1(Omega)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$uin W<^>{2,1}_{textrm{loc}}(Omega )$$end{document} is non-negative, P is a uniformly elliptic operator in non-divergent form, TH(<middle dot>)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$${mathcal {T}}_{H}(cdot )$$end{document} is certain transformation of the monotone C1documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$C<^>1$$end{document} function H(<middle dot>)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$H(cdot )$$end{document}, which is the primitive of the weight h(<middle dot>)documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$h(cdot )$$end{document}, and Thetadocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$Theta $$end{document} is the boundary term which depends on boundary values of u and del udocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$nabla u$$end{document}, which hold under some additional assumptions. Our results are linked to some results from probability and potential theories, e.g. to some variants of the Douglas formulae.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS
ISSN
1021-9722
e-ISSN
1420-9004
Volume of the periodical
32
Issue of the periodical within the volume
6
Country of publishing house
CH - SWITZERLAND
Number of pages
34
Pages from-to
nestránkováno
UT code for WoS article
001554505500003
EID of the result in the Scopus database
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