Generalizations of Stampacchia Lemma and applications to quasilinear elliptic systems. (July 2021) - Gao, Hongya; Deng, Hua; Huang, Miaomiao; Ren, Wei
Abstract: We present two generalizations of the classical Stampacchia Lemma. As applications, we consider Dirichlet problem for elliptic systems of the form − ∑ i = 1 n ∂ ∂ x i ∑ β = 1 N ∑ j = 1 n a i, j α, β ( x, u ( x ) ) ∂ u β ( x ) ∂ x j = f α, in  Ω, u ( x ) = 0, on  ∂ Ω . Under ellipticity and degenerate ellipticity conditions of the diagonal coefficients and proportional conditions of the off-diagonal coefficients, we derive some global regularity results.