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Ultracontractive Bounds for Nonlinear Evolution Equations Governed by the Subcritical p-Laplacian

  • Matteo Bonforte
  • Gabriele Grillo
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 61)

Abstract

We consider the equation Open image in new window = Δp(u) with 2 ≤ p < d on a compact Riemannian manifold. We prove that any solution u(t) approaches its (time-independent) mean ū with the quantitative bound Open image in new window for any q ∊ [2, +∞] and t > 0 and the exponents β, γ are shown to be the only possible for a bound of such type. The proof is based upon the connection between logarithmic Sobolev inequalities and decay properties of nonlinear semigroups.

Keywords

Contractivity properties asymptotics of nonlinear evolutions p-Laplacian on manifolds 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2005

Authors and Affiliations

  • Matteo Bonforte
    • Gabriele Grillo
      • 1
    1. 1.Dipartimento di MatematicaPolitecnico di TorinoTorinoItaly

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