The paper establishes refined interpolative gap bounds that guarantee higher integrability of gradients for weak solutions to inhomogeneous singular parabolic double phase equations.
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Gradient higher integrability holds for bounded solutions to parabolic double phase problems when q ≤ p + α, with a weaker interpolated gap q ≤ p + sα/(n+s) when the solution lies in C(0,T; L^s(Ω)) for s ≥ 2.
Weak solutions to the degenerate parabolic double phase equation are locally bounded.
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Bounded solutions and interpolative gap bounds for degenerate parabolic double phase problems
Gradient higher integrability holds for bounded solutions to parabolic double phase problems when q ≤ p + α, with a weaker interpolated gap q ≤ p + sα/(n+s) when the solution lies in C(0,T; L^s(Ω)) for s ≥ 2.