WEIGHTED ESTIMATES FOR NONLINEAR EQUATIONS OF DIFFERENTIAL FORMS

WEIGHTED ESTIMATES FOR NONLINEAR EQUATIONS OF DIFFERENTIAL FORMS

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 Calderón-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.