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Register a new userOptimal conditions for $L^infty$-regularity and a priori estimates for elliptic systems, I: two components
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Li Yuxiang
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In this paper we present a new bootstrap procedure for elliptic systems with two unknown functions. Combining with the $L^p$-$L^q$-estimates, it yields the optimal $L^infty$-regularity conditions for the three well-known types of weak solutions: $H_0^1$-solutions, $L^1$-solutions and $L^1_delta$-solutions. Thanks to the linear theory in $L^p_delta(Omega)$, it also yields the optimal conditions for a priori estimates for $L^1_delta$-solutions. Based on the a priori estimates, we improve known existence theorems for some classes of elliptic systems.
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In this paper, we present a bootstrap procedure for general elliptic systems with $n(geq 3)$ components. Combining with the $L^p$-$L^q$-estimates, it yields the optimal $L^infty$-regularity conditions for the three well-known types of weak solutions: $H_0^1$-solutions, $L^1$-solutions and $L^1_delta$-solutions. Thanks to the linear theory in $L^p_delta(Omega)$, it also yields the optimal conditions for a priori estimates for $L^1_delta$-solutions. Based on the a priori estimates, we improve known existence theorems for some classes of elliptic systems.
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