What the study found
The authors establish an interior gradient higher integrability result for weak solutions of degenerate parabolic double phase systems with two modulating coefficients.
Why the authors say this matters
The authors conclude that this is, to their knowledge, the first regularity result in the parabolic setting to address general double phase systems within the framework of weak solutions.
What the researchers tested
They studied 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), with 2 ≤ p ≤ q < ∞. The coefficients a(z) and b(z) are non-negative, a(z) is uniformly continuous, b(z) is Hölder continuous, and the sum a(z) + b(z) is bounded below by a positive constant.
What worked and what didn't
The paper reports that a suitable intrinsic geometry and a delicate comparison scheme were used to separate and analyze the p-phase, q-phase, and (p, q)-phase. Under the stated assumptions, this leads to the interior gradient higher integrability result.
What to keep in mind
The abstract does not describe specific quantitative estimates, examples, or applications. The result is stated for the interior and under the listed assumptions on the coefficients and exponents.
Key points
- The paper proves an interior gradient higher integrability result for weak solutions of a degenerate parabolic double phase system.
- The system includes two non-negative modulating coefficients, a(z) and b(z), with different continuity assumptions.
- The authors state that this is the first regularity result in the parabolic setting for general double phase systems in the weak-solution framework.
- The proof uses intrinsic geometry and a comparison scheme that separates p-phase, q-phase, and (p, q)-phase behavior.
Disclosure
- Research title:
- Interior gradient higher integrability for parabolic double phase systems
- Authors:
- Jehan Oh, Abhrojyoti Sen
- Institutions:
- Kyungpook National University, Goethe University Frankfurt
- Publication date:
- 2026-05-16
- OpenAlex record:
- View
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