On A.I. Koshelev’s work on regularity theory of generalized solutions of quasilinear systems of elliptic and parabolic type

摘要

This is a survey of A.I. Koshelev’s studies in the theory of regular solutions of boundary value problems, based on iterative processes converging in both the energy norm and the strong norm as well as on a priori estimates in weighted function spaces. In numerous cases, Koshelev’s estimates contain explicitly computable and sometimes sharp (unimprovable) constants. The results obtained for a broad class of problems were adapted by Koshelev to the study of boundary value problems of nonlinear elasticity and problems of hydrodynamics of viscous fluids.