We construct Green’s functions for elliptic operators of the form
in domains
, under the
assumption
or
.
We show that, in the setting of Lorentz spaces, the assumption
is both necessary and optimal to obtain pointwise bounds for Green’s
functions. We also show weak-type bounds for the Green’s function and its
gradients. Our estimates are scale-invariant and hold for general domains
. Moreover,
there is no smallness assumption on the norms of the lower-order coefficients. As applications
we obtain scale-invariant global and local boundedness estimates for subsolutions to
in the
case
.
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