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.
Author(s): Alexander Koshelev (auth.)
Series: Lecture Notes in Mathematics 1614
Edition: 1
Publisher: Springer-Verlag Berlin Heidelberg
Year: 1995
Language: English
Pages: 262
City: Berlin; New York
Tags: Analysis
Weak solutions and the universal iterative process....Pages 1-22
Regularity of solutions for non degenerated quasilinear second order elliptic systems of the divergent form with bounded nonlinearities....Pages 23-71
Some properties and applications of regular solutions for quasilinear elliptic systems....Pages 72-107
Diffeentiability of solutions for second order elliptic systems....Pages 108-174
Regularity of solutions for parabolic systems with some applications....Pages 175-215
The Navier-Stokes system; strong solutions....Pages 216-247
