An irregular complex valued solution to a scalar uniformly elliptic equation

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The method of layer potentials in Lp and endpoint spaces for elliptic operators with L∞ coefficients (2013, result): “On the other hand, specializing to the “block” case mentioned above, we o bs rve that counter-examples in [43] and [21] (along with some observations in [ 3]), show that the full range of Lp and Hardy space results treated in the present paper cannot be ob tained without assuming DG/N/M.”
Second order elliptic operators with complex bounded measurable coefficients in L p , Sobolev and Hardy spaces (2010, background): “, given any ep+ with 2n n−2 <ep+ ≤∞,there exists an operator L such that the heat semigroup {e−tL} t>0 is not bounded in L ep+. Proof. We argue as in [14], Section 1.3, but using the example of [34] rather than that of [50]. Let n ≥3. By [34], for every q <n/2 and λ >0, there is an n ×n ”
New Orlicz–Hardy spaces associated with divergence form elliptic operators (2009, background): “In this section, we recall some notions and notation on the divergence form elliptic operator, and present some basic properties on Orlicz functions and also describe some basic assumptions on them.”