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
GagliardöNirenberg inequalities The parabolic systems The elliptic systems Cross-diffusion
systems of porous media type Nontrivial steady-state solutions The duality RBMO(¿)¿H1(¿) Some
algebraic inequalities Partial regularity
