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A general class of strongly coupled elliptic systems with quadratic growth ingradients is considered and the existence of their strong solutions isestablished. The results greatly improve those in a recent paper \cite{dleJFA}as the systems can be either degenerate or singular when their solutions becomeunbounded. A unified proof for both cases is presented. Most importantly, theVMO assumption in \cite{dleJFA} will be replaced by a much versatile one thanksto a new local weighted Gagliardo-Nirenberg involving BMO norms. Examples inphysical models will be provided.

Existence of Strong Solutions to Degenerate or Singular Strongly Coupled Elliptic Systems