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Gradient higher integrability for degenerate parabolic double phase systems with two modulating coefficients
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DOI：10.1007/s00526-026-03352-y.png)
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Abstract
En 中文
We establish an interior gradient higher integrability result for weak solutions to degenerate parabolic double phase systems involving two modulating coefficients. To be more precise, we study systems of the form u(t) - div (a(z)|Du|(p-2) Du + b(z)|Du|(q-2) Du) = - div (a(z)|F|(p-2) F + b(z)|F|(q-2) F), where 2 <= p <= q < infinity and the modulating coefficients a(z) and b(z) are non-negative, with a(z) being uniformly continuous and b(z) being Holder continuous. We further assume that the sum of two modulating coefficients is bounded from below by some positive constant. To establish the gradient higher integrability result, we introduce a suitable intrinsic geometry and develop a delicate comparison scheme to separate and analyze the different phases-namely, the p-phase, q-phase and (p, q)-phase. To the best of our knowledge, this is the first regularity result in the parabolic setting that addresses general double phase systems within the framework of weak solutions.
Keywords:
REGULARITY
FUNCTIONALS
MINIMIZERS
Journal
C
IF:
2
Papers:
247
Citations:
0