We prove the Lp,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.
Bibliographical noteFunding Information:
S. Ryu was supported by NRF-2017R1C1B1010966 and NRF-2020R1C1C1A01014310.
D. Kim and K. Woo were supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2019R1A2C1084683).
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
- Embedding theorem
- Parabolic equations
- Reifenberg flat domains
- Sobolev spaces
- Unbounded lower-order coefficients
ASJC Scopus subject areas
- Mathematics (miscellaneous)