The Poincaré inequality and \(p\)-connectedness of a stratified set
Extensions of the Poincaré inequality to functions of Sobolev type on a stratified set are derived, proved and discussed. It is shown that the integrability exponents in these analogs of the Poincaré inequality depend on the geometric characteristics of the stratified set. As an application of the Poincaré inequality, the authors prove the solvability of boundary value problems for the \(p\)-Laplacian with boundary conditions of Neumann or Wentzel type. Many examples are included to demonstrate the obtained results.
scientific article; zbMATH DE number 7035747