Research Communication | Open Access
Volume 2020 | Communication ID 122 |

Existence Of Solution Of Dirichlet Problems In Markinkiewicz Space

Omar Benslimane, Ahmed Aberqi, Jaouad Bennouna
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
24 January 2020
08 February 2020
10 March 2020

Abstract: This work proves the existence solution of Dirichlet problem managed by singular convection terms : A( u ) = f( x ) in Ω. And u =0 on ∂Ω. Where A( u ) = - div ( M( x) ∇u ) + div ( u E( x )) is a Carathèodory function defined on W_0^(1,p) ( Ω ) into its dual, Ω is a bounded open subset of R^N, N > 2, E ∊ ( L^N ( Ω))^N ( vector fields ), f ∊ L^m ( Ω) with 1 ≤m