Abstract
In this paper, we establish a local higher integrability result for the gradient of a weak solution to a parabolic multi-phase equation. To achieve this, we prove parabolic Poincaré type inequalities and reverse Hölder type inequalities for the gradient of a weak solution in each of difference types of intrinsic cylinders. In particular, we formulate a delicate plan of alternatives and stopping time arguments to address the presence of two different transitions.
Original language | English |
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Pages (from-to) | 223-298 |
Number of pages | 76 |
Journal | Journal of Differential Equations |
Volume | 409 |
DOIs | |
State | Published - 15 Nov 2024 |
Keywords
- Degenerate parabolic equations
- Higher integrability
- Intrinsic cylinders
- Multi-phase problems
- Weak solution