Super and ultracontractive bounds for doubly nonlinear evolution equations.

Bonforte, Matteo, and Grillo, Gabriele. "Super and ultracontractive bounds for doubly nonlinear evolution equations.." Revista Matemática Iberoamericana 22.1 (2006): 111-129. <http://eudml.org/doc/41967>.

@article{Bonforte2006,
abstract = {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 &gt; 0 and the exponents β, γ are shown to be the only possible for a bound of such type.},
author = {Bonforte, Matteo, Grillo, Gabriele},
journal = {Revista Matemática Iberoamericana},
keywords = {Ecuaciones de evolución no lineales; Ecuaciones parabólicas; Problema de Dirichlet; Acotación; Desigualdades de Sobolev; smoothing; homogeneous Dirichlet boundary conditions},
language = {eng},
number = {1},
pages = {111-129},
title = {Super and ultracontractive bounds for doubly nonlinear evolution equations.},
url = {http://eudml.org/doc/41967},
volume = {22},
year = {2006},
}

TY - JOUR
AU - Bonforte, Matteo
AU - Grillo, Gabriele
TI - Super and ultracontractive bounds for doubly nonlinear evolution equations.
JO - Revista Matemática Iberoamericana
PY - 2006
VL - 22
IS - 1
SP - 111
EP - 129
AB - 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 &gt; 0 and the exponents β, γ are shown to be the only possible for a bound of such type.
LA - eng
KW - Ecuaciones de evolución no lineales; Ecuaciones parabólicas; Problema de Dirichlet; Acotación; Desigualdades de Sobolev; smoothing; homogeneous Dirichlet boundary conditions
UR - http://eudml.org/doc/41967
ER -