Strongly coupled (or cross-diffusion) systems of parabolic and elliptic partial differential equations appear in many physical applications. This book presents a new approach to the solvability of general strongly coupled systems, a much more difficult problem in contrast to the scalar case, by unifying, elucidating and extending breakthrough results obtained by the author, and providing solutions to many open fundamental questions in the theory. Several examples in mathematical biology and ecology are also included.

Contents

Interpolation Gagliardo–Nirenberg inequalities
The parabolic systems
The elliptic systems
Cross-diffusion systems of porous media type
Nontrivial steady-state solutions
The duality RBMO(μ)–H1(μ)|
Some algebraic inequalities
Partial regularity