Super and ultracontractive bounds for doubly nonlinear evolution equations

• Autores: Gabriele Grillo , Matteo Bonforte
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 22, Nº 1, 2006, págs. 111-130
• Idioma: inglés
• DOI: 10.4171/rmi/451
• Títulos paralelos:
  • Cotas supercontractivas y ultracontractivas para ecuaciones de evolución doblemente no lineales
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• Resumen

  • 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· = ?p(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||r? / tß for any r = q Î [1,+8) and t > 0 and the exponents ß, ? are shown to be the only possible for a bound of such type.