Abstract
We present weighted Sobolev spaces H~p,θγ(S,T) and prove a trace theorem for the spaces. As an application, we discuss non-zero boundary value problems for parabolic equations. The weighted parabolic Sobolev spaces we consider are designed, in particular, for the regularity theory of stochastic partial differential equations on bounded domains.
Original language | English |
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Pages (from-to) | 134-172 |
Number of pages | 39 |
Journal | Stochastics and Partial Differential Equations: Analysis and Computations |
Volume | 12 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2024 Mar |
Bibliographical note
Publisher Copyright:© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022.
Keywords
- Non-zero boundary value conditions
- Parabolic equations
- Traces
- Weighted Sobolev spaces
ASJC Scopus subject areas
- Statistics and Probability
- Modelling and Simulation
- Applied Mathematics