On the Hölder property for functions from the class \(B_{q,s}\)
type: Item
instance of: scholarly article
title: On the Hölder property for functions from the class \(B_{q,s}\)
zbMATH Open document ID: 0835.46034
DOI: 10.1007/BF01057459
author: Igor V. Skrypnik
published in: Ukrainian Mathematical Journal
publication date: 1994-11-10T00:00:00Z
review text: For \(\Omega\) a bounded open set in \(\mathbb{R}^n\), the author introduces a class \(B_{q, s}\) of functions \(u(x, t)\), \(x\in \Omega\), \(t\in (0, T)\) containing generalized solutions of some higher order quasilinear parabolic equations, and proves that \(B_{q, s}\) is imbedded into the space of Hölder functions. The class \(B_{q, s}\) is a subspace of \(C(0, T; L_2(\Omega))\cap L_q(0, T; W^1_q(\Omega))\) and extends the spaces \(B_2\) and \(B_q\) defined earlier by Ladyzhenskaya, Solonnikov, Uralceva \((B_2= B_{2,1})\) and Di Benedetto \((B_q= B_{q, 1})\).
Mathematics Subject Classification ID: 46E35
Mathematics Subject Classification ID: 35D10
zbMATH DE Number: 652283
zbMATH Keywords: generalized solutions of some higher order quasilinear parabolic equations
zbMATH Keywords: space of Hölder functions
reviewed by: Alois Kufner
MaRDI profile type: Publication
cites work: Q5548525
description: scientific article; zbMATH DE number 652283