Elliptic and parabolic differential inequalities
type: Item
instance of: scholarly article
zbMATH Open document ID: 0977.35150
author: Adriana Buică
publication date: 2002-01-17T00:00:00Z
Mathematics Subject Classification ID: 35R45
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35K60
Mathematics Subject Classification ID: 35B50
zbMATH DE Number: 1587903
zbMATH Keywords: comparison results
zbMATH Keywords: semilinear elliptic and parabolic inequalities
MaRDI profile type: Publication
title: Elliptic and parabolic differential inequalities
published in: Demonstratio Mathematica
review text: The author establishes comparison results for some semilinear elliptic and parabolic inequalities of the forms NEWLINE\[NEWLINE-\Delta \mu+\omega\mu\leq f(x,u)\text{ a.a. }x\in\Omega,\;u\in H^1_0(\Omega),\quad \Delta u\in L^2(\Omega),NEWLINE\]NEWLINE respectively NEWLINE\[NEWLINE\begin{aligned} & \frac{\partial \mu}{\partial t}-\Delta u\leq f(x,t,u)\text{ a.a. }x\in \Omega,\text{ all } t>0,\quad u(x,0)\leq \mu_0(x)\text{ a.a. }x\in\Omega,\\& u(\cdot,t)\in H^1_0(\Omega),\;\Delta u(\cdot,t)\in L^2(\Omega)\text{ for all }t>0,\;\frac{\partial \mu}{\partial t}\in L^1(0,T;L^2(\Omega)).\end{aligned}NEWLINE\]NEWLINE Let us mention that similar results for elliptic equations are presented by \textit{D. Gilbarg} and \textit{N. S. Trudinger} [Elliptic partial differential equations of second order, Springer, (1983; Zbl 0562.35001], but they need some continuity and differentiability for the function \(f\).
reviewed by: Viorel Iftimie
description: scientific article