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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Interpolative Refinement of Gap Bound Conditions for Singular Parabolic Double Phase Problems
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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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.
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Local boundedness for solutions to degenerate parabolic double phase problems
Weak solutions to the degenerate parabolic double phase equation are locally bounded.