Description

• Title:
  $L^\infty$-bounds of solutions for a class of strongly nonlinear elliptic equations in Musielak spaces
• Creator:
  Bourahma, Mohamed;
  Benkirane, Abdelmoujib;
  Bennouna, Jaouad;
  El Moumni, Mostafa
• Description:
  In this paper we establish the existence of bounded solutions to a strongly nonlinear elliptic problem of the form $$ -\mathop{\rm div}\mathcal{A}(x,u,{\nabla}u)+g(x,u,\nabla u)= f \quad\text{in }{\Omega}, $$ with $u\in W^1_0L_\varphi({\Omega})\cap L^{\infty}(\Omega)$, where $$ \mathcal{A}(x,s,\xi)\cdot\xi\geq \overline{\varphi}_{x}^{-1} (\varphi(x,h(|s|)))\varphi(x,|\xi|), $$% $h\colon {\mathbb{R}^+} \to \mathopen ]0,1] $ is a continuous decreasing function with unbounded primitive and $g$ is a non-linearity satisfying $|g(x,s,\xi)|\leq\beta(s)\varphi(x,|\xi|)$. We assume the $\Delta_{2}$-condition on the Musielak function $\varphi$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2020 Topological Methods in Nonlinear Analysis
• Date:
  2020.09.05
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 56, No 1 (September 2020); 129 - 160;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.011/26464 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2020.011/26465
• Subject:
  Elliptic problems;
  Musielak-Orlicz-Sobolev spaces;
  $L^\infty$-estimates;
  bounded solution;
  Primary;
  35J70;
  35J87;
  Secondary;
  46E30
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2020.011
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other