Regularity of solutions of some problems in mathematical physics (in Russian)

Abstract

The regularity of generalized solutions of boundary value problems for quasilinear systems of elliptic and parabolic partial differential equations is studied. Conditions are found under which the solutions and their derivatives are smooth (Hölder continuous) functions. Except for some natural demands, these conditions consist in the boundedness of dispersion in the spectrum of that matrix which determines the ellipticity of the considered operator.