Given a finite family of Banach function spaces over a bounded set , , and let an element of the dual of the Sobolev space . We discuss the existence, uniqueness and regularity of the solution of the linear equation under the Dirichlet or Neumann condition on the boundary of .
Our results extend recent works on very weak solution with data in weighted distance space or Lorentz space.
Cite this article
Jean-Michel Rakotoson, Linear equation with data in non standard spaces. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 26 (2015), no. 3, pp. 241–262DOI 10.4171/RLM/705