What does this research mean for the field?

Generalized Morrey space estimates hold for the gradient of weak solutions to nonlinear parabolic equations in non-smooth domains when the nonlinearity is measurable in time and exhibits small BMO characteristics in space. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

The research aims to derive generalized estimates for weak solutions of nonlinear parabolic equations in non-smooth domains.

May 31, 2026

A Priori Estimates and Regularity of Solutions to Nonlinear Parabolic Equations in Generalized Morrey Spaces

Key Points

The research aims to derive generalized estimates for weak solutions of nonlinear parabolic equations in non-smooth domains.
Developed generalized Morrey space estimates for the gradient of weak solutions.
Assumed nonlinearity is measurable in time and exhibits small BMO characteristics in space.
Applied the Crank-Nicolson method for numerical simulations of heat propagation.
Demonstrated theoretical findings through numerical simulations.
Illustrated the behavior of solutions in non-smooth domains under the modeled conditions.

Abstract

ABSTRACT In this paper, we derive generalized Morrey space estimates for the gradient of weak solutions associated with nonlinear parabolic equations in non‐smooth domains. Regarding the nonlinearity, we assume it is measurable with respect to the time variable , while exhibiting small BMO characteristics with respect to the spatial variable . In addition, we present a numerical application that models the time‐dependent propagation of heat or pressure in a subsurface environment using a parabolic PDE and the Crank‐Nicolson method, supporting our theoretical findings with visual simulations.

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A Priori Estimates and Regularity of Solutions to Nonlinear Parabolic Equations in Generalized Morrey Spaces

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Abstract

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