Weighted estimates for nonlinear equations of differential forms
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We establish weighted a priori $L^q$-regularity estimates for weak solutions to $p$-Laplacian type equations involving differential forms. These equations are analyzed under minimal assumptions on the coefficient $a(x)$, satisfying a bounded mean oscillation (BMO) type condition, and the data $F,$ belonging to weighted Lebesgue spaces with Muckenhoupt weights. By extending Calder\'on-Zygmund estimates to the weighted setting, our results provide a unified framework for studying $p$-Laplacian systems in complex scenarios, significantly broadening the scope of regularity theory in nonlinear partial differential equations.
Abstract
We establish weighted a priori $L^q$-regularity estimates for weak solutions to $p$-Laplacian type equations involving differential forms. These equations are analyzed under minimal assumptions on the coefficient $a(x)$, satisfying a bounded mean oscillation (BMO) type condition, and the data $F,$ belonging to weighted Lebesgue spaces with Muckenhoupt weights. By extending Calder\'on-Zygmund estimates to the weighted setting, our results provide a unified framework for studying $p$-Laplacian systems in complex scenarios, significantly broadening the scope of regularity theory in nonlinear partial differential equations.