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June 13, 2026Open Access

Calderón-Zygmund estimates for parabolic p-Laplacian systems with non-divergence form right-hand sides

Puntos clave

This research aims to establish Calderón-Zygmund type estimates for weak solutions in parabolic p-Laplacian systems.
Employs intrinsic scaling techniques combined with a Calderón-Zygmund type iteration scheme.
Analyzes weak solutions with p-growth and VMO coefficients.
Demonstrates the integrability transition from the right-hand side to the gradient.
Establishes that spatial gradient Du belongs to local L^s, indicating improved integrability.
Proves optimal exponents for linear case p=2 are consistent with parabolic scaling.
Confirms that right-hand side dependencies enhance the integrability of the solution.

Resumen

Abstract We establish local Calderón-Zygmund type estimates for weak solutions to nonlinear parabolic systems with p -growth and VMO coefficients. In particular, we prove that if the right-hand side belongs locally to L^ s L μ s, where the exponent μ depends explicitly on p, N, and a prescribed target exponent s>p s > p, then the spatial gradient of the solution enjoys improved integrability Du Lˢ₋₎₂ D u ∈ L loc s. The result provides a sharp transfer of integrability from the data to the gradient, consistent with the natural parabolic scaling, and recovers the optimal exponents in the linear case p=2 p = 2. The proof combines intrinsic scaling techniques with a Calderón-Zygmund type iteration scheme.

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