Some Developments on Dirichlet Problems with Discontinuous Coefficients

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Dirichlet problems with singular convection terms and applications (2015, background): “(4) To be more precise, in [2] is proved the existence of u { weak solution belonging to W 1,2 0 (Ω) ∩ L ∗∗ (Ω), if m ≥ 2N N+2 (“Stampacchia” theory); distributional solution belonging to W 1,m ∗ 0 (Ω), if 1 < m < 2N N+2 (“Calderon-Zygmund” theory); (5) where m∗ = mN N−m (1 ≤ m < N) and m ∗∗ = mN N−”