Description

• Title:
  On certain variant of strongly nonlinear multidimensional interpolation inequality
• Creator:
  Choczewski, Tomasz;
  Kałamajska, Agnieszka
• Description:
  We obtain the inequality \begin{multline*} \int_{\Omega}|\nabla u(x)|^ph(u(x))dx \\ \leq C(n,p)\int_{\Omega} \Big( \sqrt{ |\nabla^{(2)} u(x)||{\mathcal T}_{h,C}(u(x))|}\Big)^{p}h(u(x))dx, \end{multline*} where $\Omega\subset \mathbb R^n$ and $n\ge 2$, $u\colon\Omega\rightarrow \mathbb R$ is in certain subset in second order Sobolev space $W^{2,1}_{\rom{loc}}(\Omega)$, $\nabla^{(2)} u$ is the Hessian matrix of $u$, ${\mathcal T}_{h,C}(u)$ is a certain transformation of the continuous function $h(\cdot)$. Such inequality is the generalization of a similar inequality holding in one dimension, obtained earlier by second author and Peszek.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2018 Topological Methods in Nonlinear Analysis
• Date:
  2018.03.18
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 52, No 1 (September 2018); 49 - 67;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.050/14348 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2017.050/14349
• Subject:
  Interpolation inequalities;
  multiplicative inequalities;
  Sobolev spaces;
  Primary;
  46E35;
  Secondary;
  26D10
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2017.050
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other