The smoothness of solutions for quasilinear systems is one of the most important problems in modern mathematical physics. This book deals with regular or strong solutions for general quasilinear second-order elliptic and parabolic systems. Applications in solid mechanics, hydrodynamics, elasticity and plasticity are described.
The results presented are based on two main ideas: the universal iterative method, and explicit, sometimes sharp, coercivity estimates in weighted spaces. Readers are assumed to have a standard background in analysis and PDEs.