Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

On A. I. Koshelev’ Works in the Theory of Regularity of Weak Solutions for Quasilinear Elliptic and Parabolic Systems

Author(s):

M A Narbut

Universitetsky prospekt, 28,
198504, Peterhof, St. Petersburg, Russia,
Saint-Petersburg State University,
The Faculty of Mathematics and Mechanics

narbut2010@yandex.ru

Abstract:

The review of A. Koshelev’ results in the theory of regular solutions for quasilinear boundary value problems is presented. The basis of investigations made by A. Koshelev includes the iterative processes which converge both in weak and strong spaces and a priory estimates in the weighted functional spaces with given and sometimes sharp constants. The applications in the nonlinear theory of elasticity and hydrodynamics of viscous liquid are also discussed.

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