The weighted W2,p estimate on the solution of the Gellerstedt equation in the upper half space

In this note, we are concerned with the weighted W2,p estimate for the Gellerstedt equation, which is degenerate on the boundary ∂R2 +. Based on the estimates of the generalized Airy functions and Mihlin’s multiplier theorem, we establish a weighted W2,p a priori estimate. © 2006 Elsevier Inc. All rights reserved