3. Dezember 2024
Mathias Schäffner (MLU)
Regularity for quasilinear elliptic equations and applications in homogenization
I will present some regularity results for solutions of quasilinear elliptic equations. Assuming only mild monotonicity and growth conditions on the quasilinear operator, we establish higher integrability for the gradient of the solution.
The main motivation for this is that these monotonicity and growth conditions are stable under homogenization. As an application, we obtain uniform Calderon-Zygmund and Lipschitz estimates (on large scales) for p-Laplacian type operators with rapidly oscillating periodic coefficients.