Abstract
We consider the equation
= 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
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.
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© 2005 Birkhäuser Verlag Basel/Switzerland
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Bonforte, M., Grillo, G. (2005). Ultracontractive Bounds for Nonlinear Evolution Equations Governed by the Subcritical p-Laplacian. In: Rodrigues, J.F., Seregin, G., Urbano, J.M. (eds) Trends in Partial Differential Equations of Mathematical Physics. Progress in Nonlinear Differential Equations and Their Applications, vol 61. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7317-2_2
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DOI: https://doi.org/10.1007/3-7643-7317-2_2
Publisher Name: Birkhäuser Basel
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