Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T02:08:20.221Z Has data issue: false hasContentIssue false
  • English
  • Français

On solutions to the heat equation with the initial condition in the Orlicz—Slobodetskii space

Published online by Cambridge University Press:  24 July 2014

Agnieszka Kałamajska  and
Mirosłav Krbec
Agnieszka Kałamajska
Affiliation:
Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warsaw, Poland, [email protected]
Mirosłav Krbec
Affiliation:
Institute of Mathematics, Academy of Sciences of the Czech Republic, Žitná 25, CZ-115 67 Prague 1, Czech Republic
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the boundary-value problem ũt = Δxũ(x,t), ũ(x, 0) = u(x), where x ∈ Ω, t ∈ (0,T), Ω ⊆ ℝn−1 is a bounded Lipschitz boundary domain, u belongs to a certain Orlicz–Slobodetskii space YR,R(Ω). Under certain assumptions on the Orlicz function R, we prove that the solution u belongs to the Orlicz–Sobolev space W1,R(Ω × (0,T)).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 144 , Issue 4 , August 2014 , pp. 787 - 807
Copyright
Copyright © Royal Society of Edinburgh 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)