Linear equation with data in non standard spaces

  • Jean-Michel Rakotoson

    Université de Poitiers, Futuroscope Chasseneuil, France

Abstract

Given a finite family of Banach function spaces VαV_\alpha over a bounded set Ω\Omega, V=αVαV=\prod_\alpha V_\alpha, and let TT an element of the dual of the Sobolev space W2VW^2V. We discuss the existence, uniqueness and regularity of the solution of the linear equation Lu=TLu=T under the Dirichlet or Neumann condition on the boundary of Ω\Omega.

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. 241–262

DOI 10.4171/RLM/705