Abstract
We study local and global higher integrability properties for quasiminimizers of a class of double phase integrals characterized by nonstandard growth conditions. We work purely on a variational level in the setting of a metric measure space with a doubling measure and a Poincaré inequality. The main novelty is an intrinsic approach to double phase Sobolev-Poincaré inequalities.
| Original language | English |
|---|---|
| Pages (from-to) | 1233-1251 |
| Number of pages | 19 |
| Journal | Proceedings of the American Mathematical Society |
| Volume | 152 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 18 Jan 2024 |
| MoE publication type | A1 Journal article-refereed |
Funding
Part of this material was based upon work supported by the Swedish Research Council while the first author and the second author were in residence at Institut Mittag-Leffler in Djursholm, Sweden during the Research Program Geometric Aspects of Nonlinear Partial Differential Equations in 2022. The second author was partly supported by GNAMPA-INdAM Project 2022 “Equazioni differenziali alle derivate parziali in fenomeni non lineari” and by GNAMPA-INdAM Project 2023 “Regolarità per problemi ellittici e parabolici con crescite non standard”. The third author was supported by a doctoral training grant for 2022 and a travel grant from the Väisälä Fund.
Keywords
- double phase problems
- Quasiminimizers
- reverse Hölder inequalities