An existence result for linear partial differential equations with 𝐶^{∞} coefficients in an algebra of generalized functions

Abstract

We prove the existence of solutions for essentially all linear partial differential equations with C ∞ C^\infty -coefficients in an algebra of generalized functions, defined in the paper. In particular, we show that H. Lewy’s equation has solutions whenever its right-hand side is a classical C ∞ C^\infty -function.