Abstract
We present two generalizations of the classical Stampacchia Lemma. As applications, we consider Dirichlet problem for elliptic systems of the form −∑i=1n∂∂xi∑β=1N∑j=1nai,jα,β(x,u(x))∂uβ(x)∂xj=fα,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.
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