Regularity for monotone operators and applications to homogenization

I will present some regularity results for solutions of nonlinear elliptic equations. Under mild monotonicity and growth conditions on the operator, we establish higher integrability for the gradient of solutions. These conditions are particularly relevant since they are stable under homogenization. As an application, we obtain Calderón–Zygmund and Lipschitz estimates (on large scales) for p-Laplacian type operators with rapidly oscillating periodic coefficients. The results are based on joint work with Lukas Koch. If time permits, I will also discuss ongoing work (with Nicolas Clozeau and Antoine Gloria) on related questions in the setting of random coefficients.