Regularity problem for quasilinear elliptic and parabolicsystems
By: Alexander Koshelev.
Series: Lecture notes in mathematics -- 1614
Publisher: Springer
Published: 1995
Place of publication: Berlin; London
Language: eng
Number of pages: 255
Subjects: Differential equations, Elliptic -- Numerical solutions.; Differential equations, Parabolic -- Numerical equations.
Description: 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.