# Super and ultracontractive bounds for doubly nonlinear evolution equations.

Matteo Bonforte; Gabriele Grillo

Revista Matemática Iberoamericana (2006)

- Volume: 22, Issue: 1, page 111-129
- ISSN: 0213-2230

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topBonforte, 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 > 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 > 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 -

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