DIFFERENTIAL GEOMETRY/PDE SEMINAR

Wednesday, April 14 Communications 326 3:45 pm

Ljusternik-Schnirelman theorem for non-differentiable functionals

in Orlicz-Sobolev space

Matti Tienari (University of Oulu, Finland)

Ljusternik-Schnirelman theory is a generalization of the Courant minimax principle which characterizes the eigenvalues of compact and self-adjoint operators in a Hilbert space. The main result of L-S theory is the existence of infinitely many eigenvalues tending to infinity for some odd gradient operators in reflexive and separable Banach space. I shall consider functionals of calculus of variations with non-polynomial growth. The problem is that L-S theory is not directly applicable due to nonsmoothness of the functionals and nonreflexivity of the associated Orlicz-Sobolev space.