Regularity and coexistence problems for strongly coupled elliptic systems Dung LeLinh NguyenToan Nguyen 35J5535J6035B6535B45strongly coupled elliptic systemsregularityfixed point indexexistence Boundedness and H\"older regularity of solutions to a class of strongly coupled elliptic systems are investigated. The H\"older estimates for the gradients of solutions are also established. Finally, the fixed point theory is applied to prove existence of positive solution(s) for general cross diffusion elliptic systems. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.2979 10.1512/iumj.2007.56.2979 en Indiana Univ. Math. J. 56 (2007) 1749 - 1791 state-of-the-art mathematics http://iumj.org/access/