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

Autor:	Agnieszka Kałamajska, Miroslav Krbec
Rok vydání:	2014
Předmět:	Pure mathematics General Mathematics Bounded function Mathematical analysis Boundary (topology) Initial value problem Heat equation Function (mathematics) Lipschitz continuity Space (mathematics) Domain (mathematical analysis) Mathematics
Zdroj:	Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 144:787-807
ISSN:	1473-7124 0308-2105
DOI:	10.1017/s0308210513000218
Popis:	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)).
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::52a5e1024c2b5b2b6d4d423c63b4eb4f https://doi.org/10.1017/s0308210513000218 Zobrazit plný text záznamu