On the Existence of $$L^p$$ L p -Solution of Generalized Euler–Poisson–Darboux Equation in the Upper Half Space

Abstract

We focus on the existence of solution of generalized Euler–Poisson–Darboux equation, which is elliptic in $$\mathbb R^{n+1}_+$$ and has a singular coefficient on its boundary. Based on Mikhlin’s multiplier theorem and Hardy inequalities, the well-posedness of its Dirichlet problem in the upper half space is established.