Super and ultracontractive bounds for doubly nonlinear evolution equations.
We use logarithmic Sobolev inequalities involving the p-energy functional recently derived in [15], [21] to prove Lp-Lq smoothing and decay properties, of supercontractive and ultracontractive type, for the semigroups associated to doubly nonlinear evolution equations of the form u· = Δp(um) (with m(p - 1) ≥ 1) in an arbitrary euclidean domain, homogeneous Dirichlet boundary conditions being assumed. The bound are of the form ||u(t)||q ≤ C||u0||rγ / tβ for any r ≤ q ∈ [1,+∞) and t > 0 and...