A regularity result for a class of elliptic equations with lower order terms

AbstractIn this paper we establish the higher differentiability of solutions to the Dirichlet problem$$\begin{aligned} {\left\{ \begin{array}{ll} \text {div} (A(x, Du)) + b(x)u(x)=f &{} \text {in}\, \Omega \\ u=0 &{} \text {on} \, \partial \Omega \end{array}\right. } \end{aligned}$$div(A(x,Du))+b(x)u(x)=finΩu=0on∂Ωunder a Sobolev assumption on the partial map$$x \rightarrow A(x, \xi )$$x→A(x,ξ). The novelty here is that we take advantage from the regularizing effect of the lower order term to deal with bounded solutions