Optimal conditions for a priori estimates for semilinear elliptic systems with two components Original Research Article

In this paper, we present a new bootstrap procedure for elliptic systems with two unknown functions. When combined with the LpLp-LqLq-estimates, it yields the optimal L∞L∞-regularity conditions for the three well-known types of weak solutions: View the MathML sourceH01-solutions, L1L1-solutions and View the MathML sourceLδ1-solutions. Thanks to the linear theory in View the MathML sourceLδp(Ω), it also yields the optimal conditions for a priori estimates for View the MathML sourceLδ1-solutions. Based on the a priori estimates, we improve known existence theorems for some classes of elliptic systems.