Reverse smoothing effects, fine asymptotics, and Harnack inequalities for fast diffusion equations.
Disuguaglianze di Sobolev, evoluzioni nonlineari e ultracontrattività
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 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 >...
Direct and Reverse Gagliardo-Nirenberg Inequalities from Logarithmic Sobolev Inequalities
We investigate the connection between certain logarithmic Sobolev inequalities and generalizations of Gagliardo-Nirenberg inequalities. A similar connection holds between reverse logarithmic Sobolev inequalities and a new class of reverse Gagliardo-Nirenberg inequalities.
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