Description

• Title:
  On a class of intermediate local-nonlocal elliptic problems
• Creator:
  Alves, Claudianor O.;
  Corrêa, Francisco Julio S. A.;
  Chipot, Michel
• Description:
  This paper is concerned with the existence of solutions for a class of intermediate local-nonlocal boundary value problems of the following type: $$ -\rom{div} \bigg[a\bigg(\fint_{\Omega (x,r)}u(y)dy\bigg)\nabla u\bigg] = f(x,u,\nabla u ) \quad \mbox{in } \Omega, \ u\in H_{0}^{1}(\Omega ), \leqno{(\rom{IP})} $$% where $\Omega$ is a bounded domain of $\mathbb{R}^{N}$, $a\colon\mathbb{R} \rightarrow \mathbb{R}$ is a continuous function, $f\colon \Omega \times \mathbb{R} \times \mathbb{R}^{N}$ is a given function, $r> 0$ is a fixed number, $\Omega (x,r)=\Omega \cap B(x,r)$, where $B(x,r)=\{ y\in \mathbb{R}^{N}: |y-x|< r\}$. Here $|\cdot |$ is the Euclidian norm, $$ \fint_{\Omega (x,r)}u(y)dy=\frac{1}{\rom{meas}\hspace{.06em}(\Omega (x,r))}\int_{\Omega (x,r)}u(y)dy $$ and $\rom{meas}\hspace{.06em}(X)$ denotes the Lebesgue measure of a measurable set $X\subset \mathbb{R}^{N}$.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2016.12.16
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 49, No 2 (June 2017); 497 - 509;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.083/10536 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2016.083/10537
• Subject:
  Galerkin method;
  intermediate local-nonlocal elliptic problem;
  Brouwer fixed point theorem;
  45M20;
  35J25;
  34B18;
  34C11;
  34K12
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2016.083
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other