Irregular double-phase parabolic equations with non-divergence data admit unique strong solutions that transfer integrability from data to the flux, achieve higher gradient integrability, and possess second-order space regularity for all r ≥ 0 in the admissible range.
De Filippis, Gradient bounds for solutions to irregular parabolic equations with (p, q)-growth, Calc
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Global Calderon-Zygmund estimates for irregular double-phase evolution problem with non-divergence data
Irregular double-phase parabolic equations with non-divergence data admit unique strong solutions that transfer integrability from data to the flux, achieve higher gradient integrability, and possess second-order space regularity for all r ≥ 0 in the admissible range.