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Super and ultracontractive bounds for doubly nonlinear evolution equations.

Matteo BonforteGabriele Grillo — 2006

Revista Matemática Iberoamericana

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

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