Linear equation with data in non standard spaces
Jean‐Michel Rakotoson · Rendiconti Lincei Matematica e Applicazioni · 2015
Given a finite family of Banach function spaces V_\alpha over a bounded set \Omega , V=\prod_\alpha V_\alpha , and let T an element of the dual of the Sobolev space W^2V . We discuss the existence, uniqueness and regularity of the solution of the linear equation Lu=T under the Dirichlet or Neumann condition on the boundary of \Omega . Our results extend recent works on very weak solution with data in weighted distance space or Lorentz space.