Abstract:We show local and global scale invariant regularity estimates for subsolutions and supersolutions to the equation − div(A∇u + bu) + c∇u + du = − div f + g, assuming that A is elliptic and bounded. In the setting of Lorentz spaces, under the assumptions b, fand c ∈ L n,q for q ≤ ∞, we show that, with the surprising exception of the reverse Moser estimate, scale invariant estimates with "good" constants (that is, depending only on the norms of the coefficients) do not hold in general. On the other hand, assuming… Show more
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