Parabolic equations with unbounded lower-order coefficients in Sobolev spaces with mixed norms
We prove the L p , q -solvability of parabolic equations in divergence form with full lower-order terms. The coefficients and non-homogeneous terms belong to mixed Lebesgue spaces with the lowest integrability conditions. In particular, the coefficients for the lower-order terms are not necessarily...
Gespeichert in:
Veröffentlicht in: | Journal of evolution equations 2022-03, Vol.22 (1), Article 9 |
---|---|
Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Zusammenfassung: | We prove the
L
p
,
q
-solvability of parabolic equations in divergence form with full lower-order terms. The coefficients and non-homogeneous terms belong to mixed Lebesgue spaces with the lowest integrability conditions. In particular, the coefficients for the lower-order terms are not necessarily bounded. We study both the Dirichlet and conormal derivative boundary value problems on irregular domains. We also prove embedding results for parabolic Sobolev spaces, the proof of which is of independent interest. |
---|---|
ISSN: | 1424-3199 1424-3202 |
DOI: | 10.1007/s00028-022-00761-2 |