1-DIMENSIONAL HARNACK ESTIMATES


DÜZGÜN F. G. , GIANAZZA U., Vespri V.

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, cilt.9, ss.675-685, 2016 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 9 Konu: 3
  • Basım Tarihi: 2016
  • Doi Numarası: 10.3934/dcdss.2016021
  • Dergi Adı: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
  • Sayfa Sayıları: ss.675-685

Özet

Let u be a non-negative super-solution to a 1-dimensional singular parabolic equation of p-Laplacian type (1 < p < 2). If u is bounded below on a time-segment {y} x (0, T] by a positive number M, then it has a power like decay of order 2 Pp with respect to the space variable x in R x [T/2, T]. This fact, stated quantitatively in Proposition 1.2, is a "sidewise spreading of positivity" of solutions to such singular equations, and can be considered as a form of Harnack inequality. The proof of such an effect is based on geometrical ideas.