A Note on Lebesgue Solvability of Elliptic Homogeneous Linear Equations with Measure Data

In this work, we present new results on solvability of the equation A*(D) f = mu for f is an element of L-p and positive measure data mu associated to an elliptic homogeneous linear differential operator A(D) of order m. Our method is based on (m, p)-energy control of mu giving a natural characterization for solutions when 1 <= p < infinity. We also obtain sufficient conditions in the limiting case p = infinity using new L-1 estimates on measures for elliptic and canceling operators.